LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

Class 


Electric  and  Magnetic 
Measurements 


and 


Measuring  Instruments 


BY 

FRANK    W.    ROLLER,    M.E. 

v» 

MEMBER,  A.I.E.E.,  A.S.N.E.,  A.E.S.,  ETC., 


NEW   YORK 

McGRAW   PUBLISHING    COMPANY 
1907 


COPYRIGHT,  1906, 
MCGRAW  PUBLISHING   COMPANY 


PEEFACE. 

THE  following  volume  has  been  written  for  the  use  of  those 
who  have  to  do  with  electrical  and  magnetic  measurements  in 
one  form  or  another,  and  as  these  must  be  made  in  practically 
all  branches  of  the  profession,  from  the  simple  testing  out  of 
lines  and  resistances  to  the  most  elaborate  determination  of 
designs,  it  is  hoped  that  its  sphere  of  usefulness  will  be  quite 
large. 

The  subjects  have,  throughout,  been  approached  with  a  view 
toward  their  use  by  users,  not  manufacturers,  of  measuring 
apparatus,  that  is  to  say  the  book  is  in  no  sense  intended  as  a 
treatise  on  the  design  and  construction  of  instruments,  the  circle 
interested  being  decidedly  limited.  Descriptions  are,  however, 
given  of  apparatus  as  well  as  of  methods  of  test,  because  knowl- 
edge of  the  manner  in  which  a  principle  is  utilized  in  concrete 
instruments  often  suggests,  to  one  having  a  determination  to 
make  but  is  at  the  same  time  without  the  particular  form  of 
appliance  ordinarily  employed  for  that  purpose,  means  of  adap- 
ing  thereto  some  other  device  which  is  at  hand.  Further,  in 
illustrating  examples  of  instruments  for  different  kinds  of  work, 
there  has  been  in  mind  the  idea  that  these  will  enable  engineers 
to  decide,  with  the  aid  of  their  general  engineering  knowledge, 
which  are  the  best  suited  to  their  particular  requirements. 

In  line  with  the  general  idea  of  making  the  volume  of  value 
to  the  profession  at  large,  there  has  been  adopted  the  use  of  an 
appendix  which  is  thought  to  be  novel  in  character  and  to  which 
attention  is  invited.  It  will  be  seen  by  reference  thereto  that, 
without  cumbering  the  text  with  numerous  reiterations  ol  manu- 
facturers names  or  the  description  of  multitudinous  instruments 
of  a  given  class  differing  one  from  the  other  only  in  minor 

iii 


235472 


iv  PREFACE. 

detail,  those  who  are  confronted  with  the  necessity  of  procuring 
apparatus  for  making  given  tests  have  provided  a  convenient 
means  of  ascertaining  not  merely  the  names  but  also  the 
addresses  of  the  majority  of  manufacturers  of  that  particular 
kind  of  goods. 

Another  point  which  is  thought  to  be  novel  and  useful  is  the 
employment  in  diagrams  of  connection  of  the  actual  word  or 
reference  letter  that  occurs  at  each  point,  instead  of  the  more  or 
less  conventional  symbol  therefore  plus  a  reference  letter  for  the 
text.  The  author  has  used  this  system  in  his  own  work  for 
some  time  past  and  finds  it  of  decided  utility  as  a  time  saver  in 
making  sketches  and  in  the  interest  of  clearness. 

Owing  to  certain  vexatious  delays  in  connection  with  some 
of  the  illustrations,  the  issue  of  this  book  has  been  deferred^for 
a  considerable  period  after  the  completion  of  the  manuscript. 
It  is  not,  however,  thought  that  the  developments  in  the  field 
in  the  interim  have  been  of  sufficient  general  interest  or 
applicability  to  warrant  revision. 

The  author  in  conclusion  desires  to  make  acknowledgment  of 
the  courteous  services  of  Mr.  Townsend  Wolcott,  who  was  good 
enough  to  read  and  correct  a  large  portion  of  the  proofs.  - 

F.  W.  R. 

NEW  YOKK,  November,  1906. 


CONTENTS. 


PART  I. 

CHAPTER.  PAGE. 

I.     DEFINITIONS  OF  UNITS 0 1 

II.     LABORATORY  AND  COMMERCIAL  STANDARDS  OF  RESISTANCE,  CUR- 


RENT, E.M.F.,  CAPACITY,  AND  INDUCTANCE 


III.  GALVANOMETERS 38 

IV.  POTENTIOMETERS , 73 

V.     THE  MEASUREMENT  OF  RESISTANCE „ 93 

VI.     MEASUREMENT  OF  CURRENT 152 

VII.     MEASUREMENT  OF  POTENTIALS 193 

VIII.     MEASUREMENT  OF  POWER 215 

IX.     MEASUREMENT  OF  CAPACITY 234 

X.     MEASUREMENT  OF  INDUCTANCE 247 

XI.     MISCELLANEOUS  DETERMINATIONS , 257 

XII.     THE  LOCATION  OF  FAULTS 288 

PART  II. 

I.     RECORDING   INSTRUMENTS 304 

II.     INTEGRATING   METERS 324 

III.     MAXIMUM  DEMAND  METERS 339 

PART  III. 

I.     MAGNETIC  UNITS , 343 

II.     MEASUREMENT  OF  FIELD  STRENGTH 347 

III.  MEASUREMENT  OF  PERMEABILITY , 354 

IV.  HYSTERESIS 380 

APPENDIX  .                                            389 


ELECTRIC   AND   MAGNETIC    MEASUREMENTS 
AND   MEASURING   APPARATUS. 

PART  I. 


CHAPTER  I. 

DEFINITIONS   OF   UNITS. 

IN  order  to  measure  a  quantity,  condition,  or  state  of  matter, 
we  must  first  have  a  standard  of  reference.  For  although 
such  quantity,  condition,  or  state  of  one  body  can  be  compared 
directly  with  the  similar  property  of  another  body,  this  direct 
comparison  cannot  be  extended  to  three  or  more  of  them,  unless 
the  property  of  all  the  other  bodies  be  referred  to  the  said  prop- 
erty of  some  selected  one,  in  which  case  the  said  one  becomes, 
provisionally,  a  standard  of  reference.  Authorized  and  com- 
monly accepted  standards  are  called  units  ;  and  as  we  have  here 
to  deal  with  electrical  measurements,  definitions  of  electrical 
units  will  be  first  in  order. 

UNIT   OF   RESISTANCE. 

When  an  electric  current  flows  through  a  conductor  of 
electricity,  a  resistance  to  this  flow  is  always  offered  by  the 
conductor.  The  amount  of  the  resistance  is  dependent  upon 
the  material  of  the  conductor,  its  physical  condition,  geometrical 
dimensions,  temperature,  and,  under  certain  circumstances  to  be 
treated  later,  other  conditions. 

The  unit  of  resistance,  with  which  all  other  resistances  are 
compared,  is  that  which  is  offered  to  a  current  of  uniform 
strength  and  constant  direction  by  a  column  of  pure  mercury 
at  the  temperature  of  melting  ice,  having  a  mass  of  ±4.4521 
grains,  a  constant  cross-sectional  area,  and  a  length  of  106.3 
centimeters.  This  unit  is  called  the  ohm,  and  its  value  as  just 
given  is  that  determined  upon  by  the  "International  Congress 
of  Electricians,"  in  1893,  and  made  legal  in  the  United  States 

1 


MAGNETIC  MEASUREMENTS. 

by  Act  of  Congress  in  1894.  It  is  officially  designated  and 
commonly  known  as  the  "  International  Ohm "  and  is  the 
recognized  standard  to-day.  Before  the  adoption  of  the  "  Inter- 
national Ohm  "  three  other  standards  were  in  use  at  various 
times.  The  first  was  the  "Sie men's  Ohm,"  this  being  repre- 
sented by  the  resistance  offered  by  a  column  of  mercury  having 
a  cross-sectional  area  of  one  square  millimeter,  and  a  length  of 
one  meter.  The  second  unit  is  that  commonly  known  as  the 
"  B.  A.  Ohm,"  "B.  A."  being  an  abbreviation  for  "British 
Association  for  the  Advancement  of  Science,"  who  proposed  its 
adoption.  In  it  the  length  of  the  cylinder  of  mercury  is  104.8 
centimeters.  The  third  standard  adopted  was  the  so-called 
"  Legal  Ohm"  (about  which,  however,  there  was  nothing  legal), 
which  was  adopted  as  a  temporary  standard  by  an  International 
Committee,  in  1882.  It  is  represented  by  the  resistance  of  a 
column  of  mercury  having  a  cross-sectional  area  of  one  sqtiare 
millimeter  and  a  length  of  106  centimeters,  at  the  temperature 
of  melting  ice.  As  there  are  many  pieces  of  apparatus,  more 
particularly  resistance  boxes  and  Wheatstone  bridges,  calibrated 
in  the  last-named  units  still  in  use,  the  following  comparison 
table  is  given: 

TABLE    I. 

Siemen's  Ohm  =  .9408  International  Ohms. 
B.  A.  Ohm  =  .9866  International  Ohms. 
Legal  Ohm  =  .9972  International  Ohms. 

UNIT   OF    CURRENT   STRENGTH. 

The  unit  of  strength  of  electrical  current  is  called  the 
ampere.  A  current  of  one  ampere  strength  when  passed  through 
a  solution  of  nitrate  of  silver,  under  the  conditions  named  in 
the  footnote  below,  will  cause  the  deposition  of  .001118  grams 
of  silver  per  second.  This  value  of  the  ampere  is  as  defined 
by  the  International  Congress  of  Electricians,  in  1893,  already 
referred  to,  and  is  commonly  accepted  as  the  standard  to-day.* 

*  The  specification  for  the  construction  and  use  of  the  "  Silver  Voltameter" 
used  in  laboratories  as  a  primary  standard  for  determining  current  strength  is 
substantially  as  follows  :  The  voltameter  consists  in  general  of  a  platinum 
bowl  having  a  diameter  of  not  less  than  10  cm.  and  a  depth  of  4  to  6  cm., 
in  which  is  suspended  horizontally,  by  tine  platinum  wires,  a  plate  of  pure 
silver  having  an  area  of  about  30  sq.  cm.,  and  a  thickness  of  2  to  3  mm.  The 
silver  plate  is  wrapped  around  with  clean  filter  paper  secured  at  the  back  with 


DEFINITIONS  OF   UNITS.  3 

It  is,  however,  simply  the  commercial  standard  of  current,  the 
fundamental  standard  from  which  it  is  derived  being  ten  times 
as  great,  and  represented  by  a  current  of  such  strength  that  when 
passed  through  a  conductor  having  a  length  of  one  centimeter 
bent  into  an  arc  of  a  circle  having  a  radius  of  one  centimeter, 
it  will  attract  or  repel  a  unit  magnetic  pole  placed  in  the  center 
of  the  circle  with  a  force  of  one  dyne.  Later  determinations 
seem  to  show  that  1  ampere  flowing  through  a  silver  voltameter 
for  1  second  will  deposit  .001119  grams  of  silver,  instead  of 
.001118  grams,  and  that  the  International  Congress  definition 
is  that  much  in  error.  It  nevertheless  remains  in  almost  uni- 
versal use. 

UNIT    OF   ELECTROMOTIVE   FORCE. 

Electromotive  force,  commonly  abbreviated  to  E.M.F.,  is  the 
force  or  stress  which  sets  up  or  tends  to  set  up  a  flow  of  electric 
current,  just  as  in  hydraulics  pressure  tends  to  set  up  a  flow  of 
liquid.  As  the  unit  there  is  taken  that  E.M.F.  which,  contin- 
uously applied  in  a  constant  direction  to  a  circuit  having  a 
resistance  of  one  ohm,  causes  current  to  flow  at  the  rate  of  one 
ampere.  This  unit  is  called  a  volt,  and  as  defined  by  the  Inter- 
national Congress  already  mentioned,  is  represented  with  suffi- 
cient exactness  for  practical  purposes  by  ^f  f  ^  -of  the  E.M.F. 
at  15  degrees  C.  of  the  cell  known  as  the  Clark  cell,  a  descrip- 
tion of  which  will  be  given  later  (see  page  24).  It  should  here 
be  noted  that,  as  the  ampere  is  definitely  determined  and  of  a 

sealing  wax,  in  order  that  no  detached  particles  may  fall  into  the  platinum  bowl. 
A  solution  of  nitrate  of  silver,  containing  about  15  parts  by  weight  of  the  nitrate 
to  85  parts  of  water,  is  poured  into  the  platinum  bowl  to  a  depth  sufficient  to 
completely  submerge  the  silver  plate.  The  current  to  be  measured  is  passed 
through  the  voltameter  thus  formed,  entering  through  the  silver  plate  and 
departing  through  the  platinum  bowl.  The  bowl  is  thoroughly  cleaned,  dried, 
and  weighed  before  pouring  in  the  solution.  After  the  current  of  constant 
strength  has  been  passed  through  the  voltameter  for  a  given  period,  carefully 
measured  by  a  good  watch,  the  bowl  is  emptied,  thoroughly  washed,  and  dried 
with  alcohol.  It  will  be  found  on  again  weighing  the  bowl  that  it  has  gained 
in  weight,  the  added  weight  being  that  of  the  pure  silver  deposited  by  the  action 
of  the  current.  To  find  the  current  in  amperes  that  was  flowing,  divide  the 
increase  in  weight  measured  in  grams  by  the  number  of  seconds  that  the 
current  was  flowing  and  by  .001118. 

To  obtain  concordant  results  some  manipulative  skill  is  required,  and  the 
nature  of  the  voltameter  renders  experiments  expensive.  For  this  reason  this 
form  is  used  but  seldom  outside  of  the  laboratory,  and  it  is  not  thought  that  a 
sufficient  number  of  readers  will  be  interested  in  the  minutiae  to  warrant  the 
devotion  of  further  space  to  this  subject. 


4  ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

fixed  value,  the  volt  which  is  dependent  on  the  ampere  and  the 
ohm  has  not,  because  as  before  stated  the  ohm  has  had  differ- 
ent values  from  time  to  time.  The  system  under  which  the  volt 
is  measured  should  hence  always  be  stated.  If  it  is  under  the 
old  B.  A.  or  the  legal  system,  the  value  may  be  converted  into 
the  now  commonly  accepted  International  volt  with  the  aid  of 
Table  I. 

UNIT   OF   CAPACITY. 

Any  two  electric  conductors  separated  by  a  dielectric,  such 
as  air  or  any  other  nonconductor,  will  store  up  a  charge  of 
electricity  if  a  difference  of  potential  be  applied  to  them.  The 
apparatus  formed  by  the  conductors  and  the  intervening  dielec- 
tric is  called  a  condenser,  and  its  property  is  known  as  capacity. 
A  condenser  is  of  unit  capacity  when  one  volt  difference  of 
potential  applied  to  its  terminals  causes  the  flow  and  storhfg  up 
of  the  unit  quantity  of  electricity  (one  ampere  for  one  second, 
namely,  one  coulomb).  The  unit  of  capacity  as  just  defined  is 
called  the  farad.  Being  far  too  large  to  be  conveniently  used 
in  commercial  work,  the  microfarad,  which  is  one  one-millionth 
part  of  a  farad,  has  become  the  commercial  standard  for  the 
comparison  of  capacities  of  condensers,  cables,  etc. 

UNIT   OF   INDUCTANCE. 

In  addition  to  the  ohmic  resistance  offered  to  the  flow  of  the 
electric  current,  every  electric  circuit  has  another  property 
known  as  inductance  which  is  analogous  to  inertia  in  mechanics, 
and  which  opposes  any  change  in  current  strength.  This  op- 
position is  offered  for  the  following  reasons.  A  conductor 
carrying  an  electric  current  is  surrounded  by  a  magnetic  field, 
the  paths  of  whose  lines  of  force  are  circles  concentric  with  and 
whose  planes  are  at  right  angles  to  the  conductor.  The  strength 
of  the  field  is  proportionate  to  the  strength  of  the  current  and 
varies  therewith.  If,  therefore,  the  current's  strength  increases, 
an  additional  number  of  lines  of  force  is  sent  out  by  it,  and 
expanding  like  the  wavelets  in  a  pond  when  a  stone  is  thrown 
into  the  water,  cut  other  proportions  of  the  circuit.  In  accord- 
ance with  the  laws  of  electro-dynamics,  these  waves,  as  they 
cut  the  conductor,  set  up  an  E.M.F.  which  is  opposite  in  direc- 
tion to  the  E.M.F.  causing  the  current  flow,  and  therefore 


DEFINITIONS  OF   UNITS.  5 

makes  it  impossible  for  the  current  to  reach  instantaneously  the 
value  due  to  the  E.M.F.  impressed  upon  the  circuit. 

The  unit  of  inductance  is  called  the  henry,  and  is  the  induc- 
tance of  a  circuit  of  such  character  that  when  the  current 
therein  changes  in  strength  at  the  rate  of  one  ampere  per 
second,  there  is  set  up  a  counter  electromotive  force  of  one 
volto 

OHM'S  LAW. 

From  the  definition  of  a  volt  above  given  it  is  evident  that 
there  exists  a  certain  relationship  between  volts,  amperes,  and 
ohms  in  a  given  circuit.  To  state  the  law  more  concisely  than 
in  the  definition :  The  current  flowing  through  a  circuit  is  di- 
rectly proportional  to  the  E.M.Fo  impressed  thereon,  and  in- 
versely proportional  to  the  resistance  of  the  circuit.  If  we  use 
the  letter  I  to  designate  current,  the  letter  E  to  designate 
E.M.F.,  and  the  letter  R  to  designate  resistance,  the  formula 

W 

expressing  this   law  of   relationship  is,  I  =  — .     This  law  is 

±\> 

known  as  Ohm's  law  and  holds  good  when  I  is  maintained 
constant  in  value  and  direction.  Where  the  value  of  I  or  its 
direction  varies,  other  elements  enter  which  modify  this  simple 
relationship,  a  matter  which  will  be  enlarged  upon  later. 


CHAPTER  II. 

LABORATORY  AND  COMMERCIAL   STANDARDS    OF   RESISTANCE, 
CURRENT,   E.M.F.,    CAPACITY,   AND   INDUCTANCE. 

RESISTANCE    STANDARDS. 

The  Mercury    Ohm. 

As  mercury  at  the  temperature  of  melting  ice  is  a  liquid, 
and,  moreover,  readily  oxidized  when  exposed  to  air,  it  is  evi- 
dent that  the  only  way  to  make  a  standard  International  ohm 
in  accordance  with  the  specifications  laid  down  in  the  defini- 
tion is  to  enclose  the  proper  quantity  of  mercury  in  a  tube  of 
glass  or  similar  material.  The  difficulty  of  preparing  such  a 
tube  so  that  the  proper  length  holds  the  right  weight  of  mer- 
cury, of  making  contact  with  the  mercury  at  proper  points,  of 
obtaining  mercury  of  perfect  purity,  and  of  maintaining  the 
whole  apparatus  at  an  accurate  uniform  temperature,  together 
with  other  minutiae  which  must  be  taken  into  account  if  accu- 
rate, results  are  to  be  had,  evidently  call  for  considerable  care 
and  manipulative  skill  of  the  highest  order,  and  prohibit  the  use 
of  standards  so  made,  except  under  very  exceptional  circum- 
stances. 

In  Fig.  1  there  is  shown  the  standard  mercury  ohm  that  is 
used  in  the  Physikalische-Technische  Reichsanstalt,  in  Berlin. 
The  illustration  is  given  to  emphasize  the  bulk  and  real  com- 
plexity of  this  apparently  simple  apparatus.  As  can  be  gathered 
from  the  proportions,  it  is  in  the  neighborhood  of  six  feet  long. 

Even  when  a  mercury  standard  ohm  is  prepared  which  com- 
plies with  all  of  the  conditions  laid  down  in  the  official  desig- 
nation of  the  unit,  we  have  a  piece  of  apparatus  that  is  only  a 
secondary  standard,  and  not  one  directly  derived  from  fun- 
damental units  of  length,  mass,  and  time. 

Lorenz  Apparatus. 

The  standard  of  resistance  can  be  fundamentally  derived  by 
means  of  the  so-called  Lorenz  apparatus,  whose  method  of  opera- 
tion is  based  on  the  following  principle  : 

6 


STANDARDS  OF  RESISTANCE. 


8          ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

Referring  to  Fig.  2,  >&S',  is  a  coil  of  several  turns  of 
insulated  wire,  whose  diameter  is  very  accurately  measured. 
Mounted  co-axially  with  this  coil  and  within  it  is  a  metal  disc,  D, 
rotating  about  a  shaft,  0.  If  current  is  passed  through  the 
coil,  S,  lines  of  magnetic  force  flow  through  the  interior  of  the 
coil,  parallel  to  its  axis  and  cut  the  disk,  D,  in  consequence  of 
which  a  difference  of  potential  exists  between  the  center,  0, 
of  the  disk  and  its  periphery.  If  suitable  means  of  making 
contact  with  the  center  and  periphery  are  provided,  that  poten- 
tial can  be  measured  in  an  external  circuit.  PQ  is  a  bar  of 
resistance  metal  and  B  a  set  of  batteries  of  appropriate  strength, 
the  whole  being  interconnected  as  shown  in  the  diagram.  If 
now  current  be  allowed  to  flow  from  the  batteries  through  the 
coil,  $  and  bar,  PQ,  connected  in  series  therewith,  we  have  a 
drop  of  potential  along  the  bar.  If  G-  be  a  galvanometer  in- 
serted in  the  circuit  through  which  flows  the  current  cfue  to 
the  difference  in  potential  between  the  center  and  the  periphery 
of  the  rotating  disk,  and  if  the  terminals  of  that  circuit  be 
attached  to  the  bar,  PQ,  at  the  points  X,  Y,  with  the  positive 
terminal  nearest  the  positive  end  of  the  bar,  the  distance  between 
X  and  Y  may  be  varied  until  the  galvanometer  shows  that  no 
current  is  flowing  through  the  disc  circuit,  in  which  circum- 
stances the  E.M.F.  supplied  is  of  course  equal  to  that  due  to  the 
difference  in  potential  between  the  points  X  and  You  the  bar. 
Write : 

R  =  resistance  between  X  and  Y, 

I  =  current  flowing  through  the  coil  and  the  bar, 
M  =  coefficient  of  mutual  inductance  between  the 
coil  and  the  disc, 

n  =  the  speed  of  revolution  of  the  disc, 
E  =  the  E.M.F.  set  up  in  the  disc, 

then  E  =  MIn 

By  Ohm's  law,  the  difference  of  potential  between  the  points 
X  and  Y  on  the  bar  equals  RI,  and  by  hypothesis  this  also 
equals  the  E.M.F.  in  the  disc, 

hence,  E  =  MIn  =  RI,  or  R  =  Mn. 

The  resistance  between  the  points  X  and  Y  can  therefore 
be  determined  directly  by  calculation  from  the  geometrical 


STANDARDS  OF  RESISTANCE. 


9 


dimensions  of   the  apparatus  and   from   measurement   of   the 
speed  of  rotation  of  the  disc. 

It  might  seem  that  it  would  be  a  very  simple  matter  to 
measure  resistance  in  this  way,  but  as  a  matter  of  fact  it  is 
extremely  difficult  to  determine  the  dimensions  of  the  apparatus 
with  a  sufficient  degree  of  accuracy,  and  almost  impossible  to 
measure  the  speed  of  rotation  as  closely  as  is  necessary  for 
accurate  work.  These  physical  difficulties  are  so  great  that,  we 
understand,  what  is  probably  the  only  Lorenz  apparatus  on 
this  continent  has  remained  idle  for  years  because  no  one  who 
has  access  to  it  has  sufficient  leisure  or  sufficient  mechanical 


FIG.  2. 

skill  to  get  from  it  results  that  can  be  considered  as  accurate 
as  those  derived  from  a  mercury  standard. 

Metallic  Alloy  Standards. 

Practically  all  commercial  and  the  majority  of  laboratory 
standards  of  resistance  are  formed  of  wires  or  plates  of  high 
resistance,  low  temperature  coefficient,  resistance  alloy  cali- 
brated by  direct  or  indirect  comparison  with  one  of  the  stand- 
ards already  described.  Fortunately,  as  will  be  demonstrated 
later  on,  electrical  resistance  can  be  measured  with  the  highest 
degree  of  accuracy  more  easily  perhaps  than  any  other  electrical 
quantity  or  property,  and  there  are  numerous  reputable  manu- 
facturers who  are  prepared  to  supply  secondary  standards 
guaranteed  to  be  correct  within  one  fiftieth  or  even  one  one- 
hundredth  of  one  per  cent,  accompanied,  if  necessary,  by  a 


10        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

certificate  of  this  degree  of  accuracy  from  national  standardizing 
bureaus.  As  this  degree  of  accuracy  is  more  than  sufficiently 
good  for  all  commercial  purposes,  and  the  value  of  a  properly 
constructed  resistance  is  very  stable,  such  secondary  standards 
are  in  universal  use  in  commercial  work. 

The  number  of  resistance  alloys  is  exceedingly  large  and  the 
number  of  trade  names  for  them  as  varied.  Platinum  silver, 
an  alloy  of  one  part  platinum  with  two  parts  of  silver,  is  in 
extensive  use  for  fine  standards,  as  is  also  manganin,  an  alloy  of 
copper,  manganese,  and  nickel.  The  latter  alloy  is  preferable  to 
the  former  in  that  it  has  a  higher  specific  resistance  and  a  lower 
temperature  coefficient,  but  it  is  somewhat  oxidizable  and  must 
be  protected  from  atmospheric  influences  by  gilding  or  varnish- 
ing, when  in  the  form  of  small  wires  or  thin  sheets.  German 
silver,  an  alloy  of  copper,  nickel,  and  zinc,  although  frequently 
used  in  rough  commercial  resistances,  is  not  suitable  for  stand- 
ards because  of  its  comparatively  high  and  somewhat  uncertain 
temperature  coefficient.  German  silver  is  the  name  given  to  a 
great  variety  of  alloysjiaving  the  qualitative  compositions  just 
stated  but  differing  widely  in  the  quantities  of  ingredients. 
Appended  Table  II  gives  the  properties  of  several  common 
resistance  alloys. 

TABLE   II. 


Alloy. 

Resistance 
per  cm.3  in 
C.G.S.  unit 
at  0°  C. 

Temperature 
coefficient 
at  15°  C. 

Composition  in 
per  cents. 

Platinum  Silver  

31  582 

0  000243 

Pt  33°/     AP-  66°/ 

Platinum  Iridium   

30  890 

0  000822 

J.  U   00  /0,    ^Yg    UU  /0 

Pt  80  °/    Tr  20°/ 

Platinum  Rhodium  

21,142 

0.00143 

Pt  90%,  Rh  10% 

Gold  Silver  
Manganese  Steel  

6,280 
67,148 

0.00124 
0.00127 

Au  90%,  Ag  10% 
Mn  12%,  Fe  80% 

Nickel  Steel  

29,452 

0.00201 

Ni  4.35% 

German  Silver  
Platinoid  

29,982 
41,731 

0.000273 
0.00031 

Cu  50%,  Zn  30%,  Ni  20% 

Manganin  

46,678 
4,641 
2,904 

0.0000 
0.00238 
0.00381 

Cu  84%,  Mn  12%,  Ni  4% 
Al  94%,  Ag  6% 
Al  94%,  Cu  6% 

Aluminum  Silver    

Aluminium  Copper  

Copper  Aluminium  
Copper  Nickel  Aluminium 
Titanium  Aluminium  .... 

8,847 
14,912 

3,887 

0.000897 
0.000645 
0.00290 

Cu  97%,  Al  3% 
Cu87%,  Ni6.7%A16.5% 

Standards  of  resistance  made  of  solid  alloys  take  on  different 
forms  according  to  their  resistance  and  the  amount  of  current 


STANDARDS  OF  RESISTANCE. 


11 


that  they  are  to  carry.  For  accurate  work  they  must  be 
arranged  to  be  immersed  in  oil  baths,  which  will  keep  all  of  the 
parts  at  a  uniform  temperature,  which  can  be  measured  t>y  a 
thermometer  that  is  also  immersed  in  the  oil.  We  will  not 
describe  here  the  old  British  Association  form  of  standard  re- 
sistance, as  this  proved  unsatisfactory  because  of  the  difficulty 
of  determining  exactly  the  coil  temperature.  The  form  adopted 
by  the  Reichsanstalt  is  shown  in  Fig.  3.  The  resistance  wire, 
J.,  is  heavily  insulated  with  silk  and  soldered  at  its  ends  to  the 
copper  terminals,  BB.  The  long  loop  made  by  the  wire  then 


FIG.  s. 

has  its  two  sides  brought  close  together  and  is  wound  spirally 
about  the  thin  brass  cylinder,  (7,  as  shown.  This  form  of  wind- 
ing makes  the  self  inductance  very  small.  The  wire  loop  is 
purposely  made  of  a  somewhat  higher  resistance  than  th.it  to 
which  the  standard  is  to  be  adjusted  and  is  then  shunted  by 
a  fine  resistance  wire,  whose  terminals  are  likewise  soldered  to 
the  ends  of  the  rods,  BB.  If  the  fine  wire  has,  say,  one  hun- 
dred times  the  resistance  of  A  per  unit  of  length,  a  change  of 
one  inch  in  its  length  will  correspond  to  a  change  of  one  one- 


12        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

hundredth  of  an  inch  in  the  length  of  the  main  wire,  and  very 
fine  adjustments  are  thus  made  possible. 

The  resistance  unit  as  a  whole  is  placed  within  a  vessel,  D, 
filled  with  oil,  and  the  temperature  is  read  off  by  means  of  a 
thermometer  placed  therein.  It  is  common  to  supply  also  a 
stirring  apparatus  to  keep  the  oil  in  circulation,  and  to  insure 
that  all  of  the  parts  are  of  the  same  temperature. 

Resistance  standards  of  a  very  low  value  in  ohms  are  usually 
made  of  a  size  sufficient  to  carry  a  great  deal  of  current  with- 
out overheating,  as  they  are  ordinarily  wanted  to  measure 
current  in  amperes  by  observing  the  potential  drop  in  volts  at 
their  terminals  when  the  current  is  flowing.  Such  resistances 
often  take  the  form  shown  in  Fig.  4,  in  which  the  resistance 
metal  is  in  the  shape  of  strips  or  ribbons  instead  of  wires, 
electrically  connected  in  parallel  and  sweated  into  heavj*  termi- 
nal .blocks.  The  use  of  ribbons  exposes  a  large  surface  to 
the  air  for  ventilation,  and  the  end  terminals,  by  their  heat- 
conducting  properties,  assist  in  dissipating  the  heat  generated 
and  so  keeping  the  temperature  down.  A  not  generally  appre- 
ciated but  very  common  source  of  possible  error 
existing  in  resistances  made  in  this  manner  is  a 
difference  of  potential  set  up  between  the  ter- 
minal blocks  and  the  thin  blades,  by  thermo- 
electric action.  These  potentials  are  opposite, 
and  will  neutralize  each  other  if  the  tempera- 
tures at  both  ends  of  the  resistance  be  the 
same,  but  if  they  be  different,  due,  say,  to  de- 
fective soldering  of  the  blades  at  one  end,  there 
is  a  resultant  E.M.F.  at  the  terminals  secured  to  the  end  blocks 
where  the  drop  is  measured  which  is  superposed  on  the  drop  of 
potential  due  to  the  current  flow,  so  that  a  measurement  of  the 
drop  is  no  longer  a  correct  indication  of  the  current  strength. 
This  point  is  of  practical,  not  merely  academic  importance,  the 
writer  having  known  errors  in  excess  of  ten  per  cent  due  to 
this  cause. 

When  a  low  resistance  is  to  carry  an  extremely  heavy  current 
and  it  is  undesirable  to  make  the  large  investment  that  would 
be  necessary  for  the  air-cooled  form  just  described,  a  water- 
cooled  type  is  sometimes  employed.  This  often  consists  of  a 
tube  of  the  resistance  metal  equipped  with  appropriate  terminals 


STANDARDS  OF  RESISTANCE.  13 

for  connection  to  the  current  circuit,  and  with  nipples  to  which 
rubber  tubing  may  be  attached,  and  a  stream  of  water  at  a  fixed 
temperature  kept  constantly  flowing.  With  this  expedient  the 
amount  of  current  that  can  be  handled  by  the  resistance  may 
rise  as  high  as  15,000  amperes  per  square  inch  cross-sectional 
area  of  conductor  without  danger  of  overheating. 

Where  the  resistance  standards  are  to  be  of  high  value,  say 
10,000  ohms  or  more,  the  currents  that  they  are  to  carry  are 
usually  very  small  and  give  little 
trouble  from  heating.  The  re- 
sistances are  then  formed  of  very 
fine  long  alloy  wires  wound  on 
spools,  as  in  the  case  of  the  Reich- 
sanstalt  form  above  described,  but 
several  layers  deep.  For  exact 
work  they  too  must  be  immersed 
in  oil,  both  to  keep  the  tempera-  FlG-  5- 

ture  uniform  throughout  and  in  order  that  the  temperature  may 
be  measured  ;  but  for  commercial  work  of  moderate  accuracy 
this  is  superfluous.  A  convenient  form  of  high-resistance  box, 
shown  in  Fig.  5,  contains  four  coils  of  10,000,  20,000,  30,000, 
and  40,000  ohms  respectively.  The  coils  can  be  used  sepa- 
rately or  in  any  desired  combination  to  give  a  resistance  of  from 

10,000  ohms  to  100,000  ohms 
by  steps  of  10,000  ohms  value. 
With  still  higher  resistances 
it  becomes  necessary  to  take 
special  precautions  in  insula- 
ting the  coil  terminals  from 
each  other,  as  otherwise  the 
resistance  of  the  path  between 
FIG.  6.  them  offered  by  a  semi-con- 

ducting film  of  moisture  becomes  comparable  to  that  of  the 
coils  and  seriously  affects  the  accuracy. 

A  resistance  box,  containing  resistances  that  may  be  coupled 
together  to  give  a  total  resistance  of  1  megohm  and  provided 
with  special  insulating  terminals,  is  shown  in  Fig.  6.  In  this, 
as  will  be  noted,  the  contacts  are  supported  on  tall  hard  rubber 
blocks  that  greatly  increase  the  length  of  the  surface  between 
adjacent  contacts  over  which  leakage  may  take  place.  This 


14        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

particular  box  is  arranged  in  ten  groups  of  coils  of  100,000 
ohms  resistance  each,  which  may  be  interconnected  either  in 
series  or  parallel  or  any  combination  of  series  and  parallel. 
The  rubber  blocks  are  so  drilled  that  they  do  not  touch  the 
rods  connected  with  the  resistance  coils  except  at  the  top,  thus 
giving  a  very  long  leakage  surface. 

Such  wire  resistances  of  high  value  are  naturally  very  ex- 
pensive, and  the  extreme  fineness  of  the  wires  frequently  causes 
trouble,  because  they  may  become  corroded,  due  to  the  presence 
of  a  small  trace  of  acid  or  something  of  that  kind.  For  this 
reason  a  resistance  made  of  carbon,  often  in  the  form  of  a 
streak  left  by  a  soft  pencil  when  drawn  over  ground  glass,  is 
frequently  employed  when  a  resistance  having  a  value  in  the 
order  of  a  megohm  is  to  be  constructed.  Such  a  resistance  is 

shown  in  Fig.  7.  The 
"  carbon  megohms  "  are 
not  celebrated  for  their 
constancy,  however,  and 
it  is  always  advisable  be- 
fore using  one  to  compare 

FIG.  7. 

it    with    a    wire  standard 

having  a  resistance  of  10,000  ohms,  or  preferably  of  100,000 
ohms  value  by  one  of  the  methods  to  be  described  presently,  in 
order  to  determine  that  it  has  not  deteriorated. 

CURRENT    STANDARDS. 

The  Voltameter. 

In  the  definition  of  the  ampere  given  on  page  2  there  is 
stated  the  method  of  determining  the  ampere  by  means  of  the 
silver  voltameter.  This  device,  however,  is  but  seldom  used 
outside  of  a  laboratory,  both  for  the  reasons  named  and  because 
the  cost  of  the  materials  entering  into  its  construction,  when  of 
a  size  suitable  for  measuring  currents  of  some  magnitude,  is 
almost  prohibitive.  The  copper  voltameter,  in  which  the  two 
electrodes  are  of  copper,  and  the  solution  of  copper  sulphate, 
gives,  when  handled  with  reasonable  skill,  results  that  are  more 
than  sufficiently  close  for  all  commercial  purposes.  The  copper 
voltameter  is  easier  to  manipulate,  and  the  deposit  on  the  plate 
through  which  the  current  leaves  the  device  is  strongly  ad- 


STANDARDS  OF  RESISTANCE.  15 

herent;  whereas  in  the  silver  type  the  deposit  is  very  apt  to  be 
loose  enough  to  be  washed  off  when  the  platinum  bowl  is  being 
cleaned  preparatory  to  final  weighing,  unless  a  very  large  sur- 
face has  been  allowed  per  unit  of  current.  The  copper  volta- 
meter can,  further,  be  satisfactorily  used  with  current  density, 
namely,  current  per  unit  of  area  of  plate  surface,  about  five 
times  as  great  as  that  permissible  in  a  silver  voltameter,  so  the 
former  type  is  much  more  compact. 

A  serviceable  copper  voltameter  may  be  made  as  follows: 
A  containing  vessel,  usually  of  glass,  is  selected  of  sufficient 
size  to  hold  all  the  plates.  Into  this  is  poured  a  solution  of 
sulphate  of  copper  made  by  dissolving  crystals  of  pure 
sulphate  of  copper  in  distilled  water,  with  the  addition  of  a 
small  amount  (about  1  per  cent),  of  sulphuric  acid.  It  is 
essential  that  the  solution  should  be  sufficiently  acid  to  turn 
blue  litmus  paper  red.  The  solution  should  have  a  specific 
gravity  of  about  1.15,  but  this  may  be  as  low  as  1.1  or  as 
high  as  1.2  without  vitiating  results.  The  voltameter  plates  of 
pure  electrolytic  copper  are  immersed  vertically  in  this  solution. 
The  plate  through  which  the  current  leaves  the  voltameter 
must  be  carefully  cleaned,  dried,  and  weighed  before  being 
placed  in  the  cell,  in  order  that  the  gain  in  weight  may  subse- 
quently be  determined,  and  the  strength  of  the  current  flowing 
calculated  therefrom.  Where  large  currents  are  to  be  handled 

O 

several  positive  and  negative  plates  may  be  used  to  advantage, 
they  then  being  interleaved  like  the  plates  in  a  storage  battery 
cell.  No  more  than  one  ampere  per  10  sq.  cm.  of  surface 
should  be  passed  out  of  the  negative  plates,  namely,  the  ones 
through  which  the  current  leaves  the  voltameter,  and  the  posi- 
tive plates,  through  which  the  current  enters,  should  afford 
twice  this  area  for  the  same  current.  The  copper  plates  should 
preferably  be  arranged  with  one  or  two  short  strips  or  lugs  left 
attached  above,  so  that  the  current  may  be  led  to  and  from  them, 
instead  of  leaving  the  whole  plate  width  to  emerge  through  the 
surface  of  the  solution,  and  these  lugs  should  be  of  as  small  an 
area  as  is  consistent  with  their  properly  performing  their  functions. 
All  corners  and  edges  of  the  copper  plates  should  be  rubbed  off 
with  sandpaper  before  the  initial  measurement  is  attempted. 
Where  very  large  currents  are  to  be  handled  the  plates  may  be 
corrugated,  so  as  to  present  a  larger  area  for  a  given  sized  plate  ; 


16         ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


but  in  this  event  it  is  more  difficult  to  determine  with  certainty 
that  the  plates  are  clean  and  in  condition  for  use  before  being 
placed  in  the  voltameter. 

The  copper  voltameter  gives  results  that  are  dependent  both 
on  the  temperature  of  the  solution  and  on  the  current  density 
employed.  The  following  Table  III,  taken  from  the  Elec- 
trician, London,  gives  the  electrochemical  equivalent  of  copper 
for  various  conditions  of  temperature  and  current  density,  and  the 
values  there  given  must  be  used  if  accurate  results  are  to  be  had. 


TABLE  III.  —  Values 


Meikle. 


Square  Centi- 

Temperature. 

per  Ampere. 

12°  C. 

23°  C. 

28°  C. 

50 

.0003288 

.0003286 

-  V 

.0003286 

100 

.  0003288 

.0003283 

.0003281 

150 

.0003287 

.0003280 

.0003278 

200 

.0003285 

.0003277 

.0003274 

250 

.0003283 

.0003275 

.0003268 

300 

.0003282 

.0003272 

.0003262 

All  voltameters  are  more  or  less  objectionable  for  use  in 
determining  the  ampere,  for  two  reasons.  First,  they  are 
merely  more  or  less  reproducible  copies  of  a  device  which  the 
International  Congress  thought  suitable  for  the  accurate  meas- 
urement of  current  strength,  but  which  does  not  involve  determi- 
nation from  fundamental  physical  units.  Second,  they  involve, 
in  addition  to  the  element  of  current  strength,  that  of  time,  and 
a  current  must  be  kept  of  strictly  uniform  value  for  a  consider- 
able period  in  minutes  in  order  to  obtain  results.  In  other 
words,  the  voltameter  gives  the  average  value  of  the  current 
that  has  been  flowing  through  any  circuit  for  a  given  length  of 
time,  but  does  not  show  the  instantaneous  values. 

The   Tangent  Galvanometer. 

The  definition  of  the  absolute  unit  of  current  strength  states 
that  this  is  represented  by  a  current  of  such  value  that  when 
passed  through  a  conductor  having  a  length  of  1  cm.  bent  into 
the  shape  of  an  arc  of  a  circle  having  a  radius  of  1  cm.,  it  will 
attract  or  repel  a  unit  magnetic  pole  placed  at  the  center  about 


STANDARDS   OF  RESISTANCE. 


17 


which  the  radius  is  drawn  with  a  force  of  1  dyne.  It  is  hardly 
feasible  to  make  an  instrument  for  the  absolute  measurement  of 
current  based  on  this  principle,  but  the  unit  may  be  derived 
from  fundamental  measurements  of  length,  mass,  and  time  in 
other  ways. 

One  of  the  oldest  devices  for  the  accurate  determination  of 
current  strength  is  the  tangent  galvanometer,  which  is  an  instru- 
ment in  which  a  magnetized  needle  assumes  a  position  deter- 
mined by  the  resultant  of  the  action  thereon  of  the  earth's 
magnetic  field  at  a  given  point,  and  the  magnetic  force  due  to  a 
coiled  conductor  through  which  flows  an  electric  current.  The 
strength  of  the  earth's  magnetic  field  at  any  point  may  be  deter- 
mined to  practically  any  desired  degree  of  accuracy  by  means  of 
a  cumulative  method,  which  need  not  be  enlarged  upon  here. 
By  suitably  proportioning  the  diameter  of  the  coil  of  wire  to  the 
length  of  a  magnetized  steel  needle  suspended  at  its  center  so 
as  to  be  freely  rotable,  the  force  with  which  the  current  tends  to 
deflect  the  needle  by  reason  of  the  magnetic  field  surrounding 
the  conductor  will  vary  in  direct  proportion  to  the  strength  of 
the  current. 

Without  going  too  deeply  into  theory  the  action  may  be 
understood  from  the  following :  In  Fig.  8,  let  the  length  of  the 
line,,  OA,  represent  the  magnitude  of  the  force  ^  ^ 

due  to  the  earth's  magnetism  tending  to  re- 
strain the  needle,  and  the  direction  of  the  line 
represent  the  direction  in  which  it  tends  to 
hold  it,  and  let  the  line  OB,  in  a  similar  man- 
ner represent  the  magnitude  of  the  force  ex- 
erted on  the  needle  by  the  current  flowing 
through  the  coil  and  the  direction  in  which 
it  tends  to  hold  it.  This  direction  is  made 
to  be  at  right  angles  to  OA,  by  placing  the 
tangent  galvanometer  in  such  a  position  that 
the  earth's  field  holds  the  needle  at  right 
angles  to  the  plane  of  the  coil  when  no  current 
is  flowing.  From  the  law  of  the  parallelogram  A 
of  forces  the  resultant  of  the  two  forces,  OA 
and  OB,  acting  on  the  needle  will  cause  it  to  assume  the  direc- 
tion AB. 

OB,  representing  the  strength  of  the  current,  is  the  tangent 


/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

t 

/ 

18         ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

of  the  angle  OAB  through  which  the  needle  has  moved,  and 
therefore  the  tangent  of  the  angle  of  deflection  of  the  needle  is 
a  measure  of  the  current  strength.  The  strength  of  the  mag- 
netic needle  is  of  no  consequence,  as,  if  it  were  increased,  the 
action  on  it  of  the  magnetic  field  due  to  the  current  and  that  of 
the  earth's  field  would  be  increased  alike,  and  if  decreased, 
decreased  alike,  the  angular  deflection  remaining  the  same  for  a 
given  current  as  long  as  the  strength  of  the  earth's  field  remains 
constant. 

Tangent  galvanometers  are  of  value  in  that  they  enable  us 
to  derive  fundamentally  the  unit  of  current  strength ;  but  they  are 
in  very  limited  use,  as  we  have  forms  of  secondary  standards  of 
satisfactory  accuracy  and  more  convenient  of  manipulation. 
Moreover,  it  is  necessary  to  place  tangent  galvanometers  in  very 
inaccessible  locations  in  order  that  the  directive  action  014  their 
needles  due  to  the  earth's  field  may  not  be  seriously  and  con- 
stantly disturbed,  in  ever  changing  degree,  by  the  other  magnetic 
fields  due  to  electric  currents  such  as  are  in  use  in  every  civilized 
community. 

The  Ampere  Balance. 

A  different  class  of  apparatus  in  wide  use  as  a  standard  for 
the  measurement  of  electric,  current  is  the  ampere  balance,  the 
most  generally  known  example  of  which  is  that  invented  by 
Lord  Kelvin.  While  this  must  primarily  be  calibrated  with  the 
aid  of  a  silver  or  copper  voltameter,  or  a  tangent  galvanometer, 
it  contains  no  parts  liable  to  change  under  proper  usage,  and 
has  the  great  advantage  that  it  indicates  the  current's  strength 
at  every  instant,  not  the  product  of  the  average  current  by  the 
time  that  it  has  been  flowing  as  in  the  case  of  the  voltameter. 
It  is,  further,  simple  of  manipulation  considering  that  it  is  a  stan- 
dard. The  apparatus  is  based  on  the  well-known  law  that  cur- 
rents flowing  in  the  same  direction  in  parallel  adjacent  conduc- 
tors attract  each  other,  and  those  flowing  in  opposite  directions 
in  parallel  adjacent  conductors  repel  each  other,  and  that  the 
forces  of  attraction  and  repulsion  at  a  given  fixed  distance  are  in 
direct  proportion  to  the  squares  of  the  strength  of  the  currents. 

It  is  evident  that  in  an  apparatus  embodying  this  principle 
one  of  the  conductors  must  be  freely  movable  in  order  that 
any  tendency  to  change  in  relative  positions  may  at  once  be 


STANDARDS  OF  RESISTANCE.  19 

observed  by  suitable  means  and  equilibrium  restored  by  the 
application  of  appropriate  restraining  forces.  There  is  some 
difficulty  in  providing  a  means  for  making  electrical  connection 
with  a  movable  conductor  which  will  carry  considerable  current 
and  at  the  same  time  be  perfectly  flexible.  In  the  Kelvin 
apparatus  this  problem  was  solved  as  follows :  Referring  to 
the  diagrammatic  perspective  in  Fig.  9,  T  and  T'  are  pairs  of 
semi-cylinders  of  brass,  the  upper  ones  of  which  are  rigidly 
secured  to  the  base  frame  of  the  instrument.  To  the  upper 
surfaces  of  the  upper  pairs  far  back  from  the  edge  are  sold- 
ered a  large  number  of  exceedingly  fine  copper  wires,  which 
are  combed  out  to  be  parallel  with  each  other  and  then  led  over 
the  rounded  surfaces  of  the  upper  semi-cylinders,  across  the 


/•" 


FIG.  9. 

short  gap  separating  them  from  the  lower  semi-cylinders  and 
nearly  around  the  latter  where  they  are  finally  soldered  in  place 
in  a  similar  way.  These  fine  wires,  or  ligaments  as  they  are 
called,  serve  both  to  sustain  the  movable  conductor  and  as  a 
means  of  conveying  the  current.  Their  flexibility  alone  would 
enable  the  coils  of  wire,  MM' ,  to  swing  about  the  point  of  sus- 
pension with  perfect  freedom  ;  but  making  the  surfaces  cylin- 
drical gives  an  additional  factor  of  assurance  that  there  shall 
be  no  restraining  due  to  the  bending  of  the  ligaments,  in  that 
the  cylinders  allow  a  kind  of  rolling  motion  which  greatly 
decreases  any  opposition  to  motion  that  the  almost  inappreciable 
rigidity  of  the  ligaments  might  tend  to  offer. 

Having  now  a  pair  of  coils,  MM',  at  the  opposite  ends  of  a 
freely    suspended    lever    and    through    which  current  may  be 


20        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

passed,  all  that  is  necessary  in  order  to  have  the  elements  of  a 
complete  measuring  instrument  is  a  set  of  stationary  coils  simi- 
lar to  the  freely  suspended  ones  and  placed  parallel  thereto,  to- 
gether with  a  suitable  measurable  restraining  force  to  keep  the 
movable  coils  in  a  position  of  equilibrium  when  current  is  passed. 
In  the  actual  instrument,  two  stationary  coils  are  used  in  con- 
nection with  each  movable  one ;  all  being  interconnected  so  that 
at  the  right-hand  end  of  the  apparatus  the  reaction  between  the 
upper  stationary  coil  and  the  movable  one  tends  to  move  the 
latter  in  one  direction  and  the  lower  stationary  coil  assists  in  that 
action,  the  stationary  coils  on  the  other  end  of  the  apparatus 
being  coupled  in  a  reverse  manner,  the  sum  total  of  all  of  the 
efforts  thus  being  to  cause  the  lever  to  go  downward  at  one  end  or 
the  other.  In  the  figure,  the  connections  are  such  that  the  left- 
hand  end  of  the  balance  tends  to  rise  when  current  is  applied. 
As  the  direction  of  current  flow  is  opposite  in  the  two  halves  of 
the  instrument,  it  can  be  seen  that  if  the  whole  apparatus  is 
placed  in  a  uniform  magnetic  field,  such  as  the  earth's  field,  the 
results  will  not  be  vitiated;  as  any  tendency  to  a  decreased  or 
increased  effort  on  one  arm  of  the  balance,  because  of  the  pres- 
ence of  that  field,  is  offset  by  the  decreased  or  increased  force 
exerted  by  the  other  half.  An  apparatus  that  is  made  indepen- 
dent of  the  influences  of  outside  magnetic  fields,  by  composing 
it  of  halves  equally  and  oppositely  affected  by  such  fields,  is  said 
to  be  astatic. 

The  measurable  restraining  force  applied  to  hold  the  movable 
element  of  the  balance  in  a  position  of  equilibrium  is  supplied 
by  a  movable  weight,  whose  distance  from  the  fulcrum  of  the 
balance  arm  is  adjustable.  An  index  finger  is  attached  to  the 
movable  element,  so  that  its  position  relative  to  a  fixed  mark 
maybe  observed  and  the  fact  that  equilibrium  exists  established. 
These  details  are  shown  in  Fig.  10  where  Jis  the  index  finger, 
D  the  fixed  scale,  and  R  the  movable  weight  sliding  along  the 
movable  arm,  P.  Only  one  of  the  trunions,  T,  supporting  the 
movable  arm  is  shown.  It  will  be  noted  from  the  illustration 
that  the  apparatus  is  provided  with  two  scales,  one  of  them 
having  equally  spaced  divisions  and  the  other  in  which  the 
spaces  between  the  scale  markings  progressively  increase  in 
size  from  zero  on.  The  equal  scale  shows  the  distance  that  the 
movable  weight,  72,  has  been  moved  and  the  non-equal  one,  the 


STANDARDS  OF  RESISTANCE.  21 

current's  strength,  which  can  thus  be  read  off  directly  from 
the  position  of  the  weight.  It  will  be  noted  that  the  zero  of 
the  scales  is  not  in  the  center,  as  would  be  the  case  if  the  ordi- 
nary mechanical  balance  arrangement  were  employed,  but  at 
the  extreme  left-hand  end.  This  feature  is  made  possible  by 
the  following  plan :  At  the  right-hand  end  of  movable  element 
there  is  secured  the  trough,  A,  in  which  is  placed  a  certain 
definite  weight  that  is  just  sufficient  to  counterbalance  the 
weight  of  the  movable  piece,  R,  when  that  piece  stands  at  zero 
on  the  scales.  During  that  part  of  the  path  of  R  included 
between  the  zero  and  the  point  opposite  to  the  fulcrum,  II  is 
opposed  to  the  weight  placed  in  A,  and  their  difference  is  the 


FIG.  10. 

force  balancing  the  pull  of  the  current.  At  the  center  of  the 
scale,  the  opposing  force  is  that  due  to  the  weight  in  A  only, 
and  from  that  point  on  to  the  extreme  right-hand  end  of  the 
scales  that  due  to  the  sum  of  the  moments  (weight  times  dis- 
tance from  the  fulcrum)  of  R  and  A.  The  scale  that  is  not 
equally  divided  is  attached  to  the  stationary  portion  of  the 
instrument,  and  from  it  ampere  values  may  be  read  off  directly. 
The  equally  divided  scale  is  part  of  the  movable  balance  arm, 
and  is  supplied  because  it  is  easier  to  estimate  correctly  the 
value  of  a  fraction  of  scale  division  when  all  divisions  are  of 
uniform  value  than  of  a  division  in  a  series  which  is  progressively 
increasing  or  decreasing.  The  latter  scale  is  used  only  when 


22        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

exact  measurements  are  to  be  made,  and  the  value  of  the  cur- 
rent then  computed  with  the  assistance  of  tables  that  come  with 
the  instrument  and  which  give  the  doubled  square  roots  directly. 
The  balances  are  provided  with  glass  covers  to  shield  them 
from  draughts,  and  the  movable  weight,  R,  is  slid  along  the 
balance  arm  through  the  aid  of-  a  carriage,  B,  which  may  be  oper- 
ated from  outside  by  means  of  silk  cords,  (7(7,  the  whole  being  so 
arranged  that  no  part  of  the  weight-moving  device  is  in  contact 
with  the  weight  when  the  cords  are  released,  thus  obviating  any 
chance  of  error  due  to  friction  between  the  pusher  and  the 
weight.  These  balances  are  made  in  a  variety  of  sizes  suitable 


FIG.  ll. 

for  measuring  currents  as  low  as  .025  amperes  to  as  high  as 
2500  amperes.  They  are  particularly  valuable  in  that  they 
may  be  used  to  measure  alternating  currents  as  well  as  direct 
currents,  the  wire  windings  in  the  large  sizes  being  composed 
of  cables  of  many  fine  insulated  wires  in  parallel,  so  as  to  insure 
proper  and  uniform  distribution  of  current  irrespective  of 
inductive  influences. 

It  has  become  of  late  the  fashion  in  some  quarters  to  ridicule 
the  Kelvin  balances  because  they  are  somewhat  tedious  to 
manipulate  as  compared  with  direct  reading  meters  of  commer- 
cial patterns  to  be  described  in  a  latter  chapter,  because  they 


STANDARDS  OF  RESISTANCE.  23 

are  not  portable,  and  because  it  takes  some  time  for  a  balance 
to  be  obtained,  as  the  period  of  oscillation  of  the  movable  element 
is  very  long,  approximately  three  or  four  seconds.  It  is  true 
that  all  of  these  objections  exist ;  but,  on  the  other  hand,  the 
apparatus  contains  110  parts  liable  to  change,  except  the  windings 
themselves,  which  might  deteriorate  if  heavily  overloaded,  they 
have  exceptionally  long  scales,  they  are  astatic,  and  good  on  both 
direct  and  alternating  current.  The  latter  quality  renders  them 
specially  valuable  in  the  accurate  measurement  of  alternating 
current  by  transfer  methods  and  in  the  calibration  of  alternating 
instruments. 

Other  forms  of  balances  have  been  devised  from  time  to  time, 
notably,  the  Pellat  balance,  shown  in  Fig.  11.  In  this  there  is 
but  one  stationary  and  but  one  movable  coil  which  are  arranged 
at  right  angles  to  each  other.  The  current  is  led  into  and  out 
of  the  latter  through  fine  spirals  of  silver,  which  afford  but  little 
opposition  to  its  movement,  and  a  scale  pan  with  weights  is 
used  to  supply  the  restraining  force. 

The  Potentiometer. 

Another  method  of  accurately  measuring  a  current  is  to  pass 
it  through  a  known  standard  resistance  and  measure  the  re- 
sultant drop  in  potential.  If  the  current  is  continuous  the 
most  suitable  instrument  for  this  method  of  measurement  is 
the  potentiometer.  As  a  special  chapter  (see  page  73)  has 
been  devoted  to  this  instrument  and  its  uses,  the  reader  is 
referred  to  it  for  a  description  of  this  very  satisfactory  method 
of  current  measurement. 

ELECTROMOTIVE    FORCE    STANDARDS. 

Determination  ly  Drop  of  Potential. 

The  definition  of  the  volt  suggests  a  practicable  method  of 
establishing  this  unit.  We  have  only  to  pass  a  current  of 
known  strength  through  a  known  standard  resistance  when  the 
difference  of  potential  at  the  terminals  of  the  resistances  ca^  be 
calculated  from  Ohm's  law,  E  =  EL  In  measuring  E.M.F.  in 
this  way,  it  must  be  borne  in  mind  that  unless  the  device  that 
indicates  the  voltage  is  of  practically  infinite  resistance,  R  in  the 
formula  is  not  the  resistance  of  the  standard  resistance  coil  but 


24        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

that  of  the  circuit  formed  by  the  coil  shunted  by  the  measuring 
apparatus  attached  to  its  terminals.  In.  Fig.  12  herewith,  let  B 
re  present  a  source  of  current,  and  .A  represent  a  balance  or  other 
device  for  accurately  measuring  the  current  strength,  R  the 
standard  resistance,  whose  value  may  be  assumed  to  be  one  ohm, 
and  V  the  device  that  indicates  the  voltage.  When  V  is  not 
attached  to  11,  the  difference  of  potential  between  the  terminals 
rand  /  of  the  latter,  when  one  ampere  is  flowing,  is  from  Ohm's 
law,  one  volt.  Assume  that  the  resistance  of  J^is  49  ohms.  If 
this  is  now  connected  to  the  terminals  of  J?,  the  resistance  be- 
tween the  points  r  and  /  is  no  longer  1  ohm,  but  from  the  law 
of  divided  circuits  (see  page  93)  .98  ohm,  and  the  difference  of 
potential  with  one  ampere  flowing  .98  volt  instead  of  one  volt, 

B 


ff(  I-  Ohm.} 


V  (49 Ohms) 


FIG.  12. 


or  an  error  of  2%.  Therefore,  if  V  is  of  a  resistance  compara- 
ble with  that  of  the  standard  resistance  coil,  the  value  of  its 
resistance  must  be  known  and  allowed  for,  in  accordance  with  the 
above  illustration.  With  the  aid  of  the  potentiometer,  measure- 
ments may  be  made  without  necessitating  this  correction,  as  will 
develop  later  in  the  chapter  devoted  to  this  instrument. 

Standard  Cells. 

The  Clark  Cell.  —  According  to  definition  the  International 
volt  is  an  E.M.F.  whose  value  is  represented  with  sufficient  ac- 
curacy for  practical  purposes  by  -i|  -|  |  of  the  E.M.F.  between 
the  terminals  of  the  battery  known  as  the  "  Clark  Cell."  The 
Clark  cell  is  one  in  which  the  negative  electrode  is  a  pure  zinc 
rod  or  amalgam  of  zinc  and  mercury,  the  positive  electrode  pure 
mercury,  and  the  electrolyte  a  saturated  solution  of  pure  mer- 


STANDARDS  OF  RESISTANCE. 


25 


curous  sulphate  and  zinc  sulphate.  Many  precautions  must  be 
taken  in  the  preparation  of  the  materials  forming  this  cell  so  that 
they  may  be  of  sufficient  purity,  and  considerable  skill  is  re- 
quired in  putting  such  a  cell  together.  As  they  may  be  pur- 
chased from  numerous  manufacturers  who  have  the  requisite 
facilities,  the  detailed  instructions  for  constructing  them  will 
not  be  given  here.  Those  who  are  interested  may  refer  to  the 
report  of  the  International  Congress  which  selected  the  cell  as 
a  standard,  or  the  fairly  complete  abstracts  which  will  be  found 
in  Fleming's  "  Handbook  for  the  Electrical  Laboratory  and 
Testing  Room,"  Carhart's  "  Electrical  Measurements,"  etc. 
The  cell  is  usually  set  up  in  small  glass  tubes  having  a  diame- 
ter of  about  f  of  an  inch  and  a  depth  of  H  to  2  inches,  the 


Maiine  Glue 


Glass  Tube 


Platinum  Wire 


Glass  Cell 


Zinc  sulphate  Paste 


Mercury 


FIG.  13. 

elements  being  often  arranged  as  shown  in  Fig.  13.  This  is 
the  original  form  of  the  Clark  cell,  and  is  objectionable  for  the 
following  reasons :  It  is  not  portable,  as  its  inversion  would 
cause  the  mercury  to  contaminate  the  zinc,  the  electrolyte  must 
be  kept  concentrated,  and  when  the  temperature  rises  it  takes 
a  considerable  length  of  time  for  the  solution  again  to  become 
saturated.  The  latter  fault  is  particularly  serious,  as  it  means 
that  there  is  a  lag  of  several  hours,  or  perhaps  days,  before  the 
E,M.F.  will  correspond  with  that  of  a  normal  cell  at  the  new 
temperature. 


26       ELECTRIC  AND    MAGNETIC  MEASUREMENTS. 

To  insure  that  all  portions  of  the  cell  may  quickly  attain  any 
new  temperature,  Mr.  Hamilton  has  adopted  the  expedient  of 
precipitating  chemically  a  thin  film  of  silver  on  the  outside  of 
the  glass  containing  tube  and  then  heavily  plating  this  coating 
with  copper.  Copper,  of  course,  is  an  excellent  heat  conductor, 
and  since  it  is  in  such  intimate  contact  with  the  glass,  the 
attainment  of  a  new  temperature  throughout  the  cell  is  greatly 
accelerated. 

The  difficulty  due  to  the  presence  of  a  large  mass  of  free 
mercury  may  be  overcome  by  the  use  of  an  electrode  which  con- 
sists of  a  flattened  spiral  of  platinum  wire  amalgamated,  either 
by  electrolytic  methods,  or  by  heating  to  redness  and  plunging 
into  mercury.  By  virtue  of  capillary  attraction  this  spiral  will 
take  up  and  hold  enough  mercury  between  its  convolutions  to 
make  it  an  excellent  electrode.  It  performs  its  functions  well 
that  the  tube  may  be  inverted  or  even  sent  through  the  mails 
without  shaking  any  of  the  mercury  loose.  The  use  of  such 
amalgamated  spirals  is  due  to  Dr.  Muirhead.  A  cell  of  this 
form,  according  to  the  International  Congress,  has  an  E.M.F. 
of  1.434  true  volts.  If,  however,  we  use  the  later  and  more 
generally  accepted  chemical  equivalent  of  silver,  .001119,  in- 
stead of  .001118,  as  used  by  the  said  Congress  in  defining  the 
value  of  the  ampere,  the  E.M.F.  of  the  Clark  cell  is  1.4327 
volts,  a  value  which  is  now  used  abroad  and  is  probably  more 
nearly  correct. 

Another  form  of  cell  better  than  the  original  Clark  cell  is  a 
modification  devised  by  Professor  Callender,  which  is  often 
called  the  Inverted  Clark  Cell.  In  this  the  order  of  the  ele- 
ments entering  into  the  construction  is  reversed  and  the  lag 
between  the  temperature  of  the  cell  and  the  E.M.F.  is  nearly 
absent. 

The  Carhart- Clark  Cell  —  The  Carhart-Clark  cell,  a  form  that 
is  widely  used  in  this  country,  is  shown  in  section  in  Fig.  14. 
The  figure  shows  a  globule  of  metallic  mercury  used  for  one  pole, 
but  it  is  not  uncommon  to  use  the  amalgamated  platinum  spiral 
described  above.  The  paste  of  mercurous  sulphate  is  separated 
fr  mi  the  zinc  by  a  wad  of  asbestos  on  which  the  zinc  rests. 
The  most  important  change  from  the  original  Clark  form  is 
in  the  use  of  a  zinc  sulphate  solution  that  is  not  kept  saturated 
at  all  temperatures,  but  on  the  contrary  is  saturated  only  when 

V 


STANDARDS  OF  RESISTANCE. 


27 


the  temperature  falls  to  0°  C.,  at  which  temperature  no  cell  is 
ever  used  in  practice.     No  time  is  therefore  expended  in  wait- 
ing for  the  solution  to  become   satu- 
rated if  the  temperature  should  rise, 
and  there  is  no  consequent  increase 
of  solution  density  that  lowers  the 
E.M.F.     This  cell  not  only  responds 
far    more    quickly    to     temperature 
changes,  but  has  a  lower  temperature 
coefficient    which    figures    out    just 
about  one  half  of  that  of  the  original 
Clark  form.     Professor  Carhart  gives 
the  formula  connecting  the  tempera-    Asbesto> 
ture  and  E.M.F.  as 


Seal 


=  1.4401  -.0004     - 


Soluti 
ZnS04 


Zrt 


Hg,S04 

Paste 


FIG.  14. 


this    being    correct   at  temperatures 
around  15°  C. 

A  drawback  to  these  and  all  other  standard  cells  containing 
non-saturated  solutions  is  that,  if  improperly  sealed,  the  evapora- 
tion of  the  liquid  causes  a  change  in  concentration,  with  a 
resultant  change  in  E.M.F. 

Cadmium  Cells.  —  The  comparatively  high  temperature  coef- 
ficient of  the  Clark  cell  led  many  experimenters  to  investigate 
other  combinations  that  would  be  equally  reliable,  but  in 
which  this  drawback  would  be  less  prominent.  The  best  is 
probably  that  patented  by  Weston  (U.  S.  Patent  No.  22,482 
of  1891).  It  is  similar  in  all  respects  to  the  Clark  cell,  except 
for  the  fact  that  cadmium  is  used  instead  of  zinc  and  cadmium 
sulphate  instead  of  zinc  sulphate.  According  to  the  specifica- 
tions, this  cell  has  a  temperature  coefficient  of  but  .018  percent 
per  degree  C.,  this  being  only  one  fourth  of  the  temperature  coeffi- 
cient of  the  Carhart-Clark  cell,  and  one  eight  of  that  of  the  original 
Clark  cell.  Its  E.M.F.  is  given  as  1.019  volts.  The  Reichsanstalt 
in  Berlin  have  carefully  tested  this  type  of  cell  and  recommend  the 
form  shown  in  Fig.  15.  Its  H -shape  is  that  suggested  in  18Q5  by 
Lord  Rayliegh  for  the  Clark  cell,  and  frequently  used  for  that 
purpose.  The  preparation  of  the  materials  and  the  assemblage 
of  the  cell  calls  for  the  same  minute  observation  of  details,  as 
is  the  case  with  the  Clark  cell  in  any  of  its  forms. 


28        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

Care  and  Use  of  Standard  Cells.  —  Standard  cells  form  a  most 
valuable  basis  for  the  accurate  measurement  of  potential  and 
current  for  both  laboratory  and  commercial  conditions,  and  they 
should  be  more  generally  used  than  they  are.  It  is  not  recom- 
mended that  the  user  attempt  to  make  his  own,  in  fact  the 
results  in  that  event  would  probably  be  very  unsatisfactory, 
but  the  cells  themselves,  as  before  stated,  can  be  easily  and 
inexpensively  purchased  in  many  quarters.  They  are  by  no 
means  the  delicate  fussy  devices  that  they  have  somehow  the 
reputation  of  being ;  on  the  contrary,  they  are  really  very 
rugged  and  will  stand  an  incredible  amount  of  misuse  without 
injury.  The  writer  has  even  known  of  one  being  dead-short 


Cadmium 
Sulphate 
Crystals 


FIG.  15. 

circuited  for  an  appreciable  interval,  certainly  as  long  as  two 
minutes,  after  which  the  potential,  although  at  first  far  below 
normal,  rapidly  rose,  and  after  the  expiration  of  several  hours 
again  became  normal.  The  power  of  the  form  in  which  the 
amalgamated  platinum  spiral  is  used  to  withstand  tumbling 
about  has  already  been  mentioned. 

It  must  always  be  borne  in  mind  that  these  standard  cells 
give  their  stated  E.M.F.  only  on  open  circuit,  namely,  when  not 
delivering  any  current.  When,  therefore,  they  are  attached  to 
the  terminals  of  a  commercial  form  of  voltmeter  (all  of  which,  as 
explained  further  on,  require  current  for  their  operation),  the 
resulting  indication  will  be  meaningless.  Students  seem  to  be 
particularly  prone  to  attacli  a  standard  cell  to  the  low-reading 
coil  of  a  commercial  voltmeter  having  a  resistance  that  is  almost 


STANDARDS  OF  RESISTANCE. 


29 


as  low  as  that  of  the  cell  itself,  with  the  result  that  the  voltage 
indicated  by  the  instrument  will  steadily  and  rapidly  continue 
to  fall  until  nearly  zero  because  of  the  polarization  due  to 
the  current  output  that  is  demanded.  To  guard  against  this 
abuse  it  is  usual  to  build  into  the  base  of  the  case  containing  a 
standard  cell,  such  as  is  shown  in  Fig.  16,  a  high  resistance  of  a 
value  of  at  least  10,000  ohms,  connected  permanently  between 
one  battery  terminal  and  its  binding  post,  so  that  it  is  im- 
possible under  any  circumstances  to  dead-short  circuit'  the 
apparatus. 

The  device  that  is  almost  al ways  used  for  determining  E.M.F. 
in  terms  of  the  E.M.F.  delivered  by  a  standard  cell  is  the  poten- 
tiometer.     With  this   the  E.M.F.  is 
measured  when  the  cell  is  not  deliv- 
ering current ;    all  of    which  will  be 
explained    in   greater    detail    in    the 
chapter  devoted  to  that  instrument. 

The  Daniell  Standard  Cell.  —  In 
the  event  that  a  Clark  cell  is  not 
available,  the  ancient  and  honored 
copper,  copper  sulphate,  zinc  sulphate, 
and  zinc  Daniell  cell  can  be  made  up 
as  a  standard  having  no  mean  pre- 
tension to  accuracy.  To  make  one 
there  is  required  a  glass-containing 
vessel,  usually  an  ordinary  batter 
jar,-  a  small  porous  cup  (say  two 
inches  in  diameter  by  four  inches 
deep),  a  rod  of  commercially  pure  zinc  carefully  cleaned  with 
sandpaper  and  subsequently  amalgamated  with  mercury,  a  strip 
of  pure  electrolytic  copper  of  any  convenient  dimensions  (say 
one  inch  broad  and  five  or  six  inches  long),  a  solution  of 
chemically  pure  zinc  sulphate  of  a  specific  gravity  of  1.200 
(555  parts  by  weight  of  zinc  sulphate  crystals  to  445  parts 
of  distilled  water  will  give  this  density),  and  a  saturated  solu- 
tion of  chemically  pure  copper  sulphate  in  distilled  water  w  th 
the  copper  sulphate  present  in  excess.  Both  the  zinc  rod  and 
the  copper  strip  must,  of  course,  be  provided  with  suitable 
terminals  for  the  attachment  of  the  circuit  wires.  It  is 
advisable  to  plate  the  copper  strip  with  a  coating  of  electro- 


FlG.  16. 


FIG.  18. 


30        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

lytic  copper  just  before  using  it,  either  by  making  it  the 
anode  in  a  regular  plating  bath  or  by  short  circuiting  the  cell  on 
itself,  in  which  case  the  copper  plate  becomes  automatically 
coated  with  electrolytic  copper. 

The  copper  strip  is  placed  in  the  porous  cup  and  the  cup  is 
almost  filled  with  the  copper  sulphate  solution.  The  porous  cup 
is  then  placed  in  the  glass-containing 
jar  and  the  zinc  solution  poured  around 
it  until  the  level  of  its  surface  is  prac- 
tically on  the  same  plane  as  the  level  of 
the  copper  sulphate  in  the  porous  cup. 
The  zinc  rod  is  then  placed  in  the  zinc 
sulphate  solution,  and  the  cell  as  a  whole 
is  ready  for  use. 

Such  cells  have  an  E.M.F.  of  1.072 
volts,  and  are  of  extremely  low  internal 
resistance  so  that  they  may  furnish  an 
appreciable  amount  of  current.  They 
do  not  polarize  readily,  and  have  a  very  low  temperature  coeffi- 
cient. With  reasonable  care  in  selecting  the  materials,  these 
cells  may  be  relied  upon  to  be  accurate  within  about  one  fifth  of 
one  per  cent.  A  cell  of  this  kind  is  shown  in  section  in  Fig.  18. 

Electrostatic    Voltmeters. 

Referring  to  Fig.  19,  if  aa  be  two  box-shaped  metallic 
sectors,  bb  a  movable  paddle -shaped  conductor,  and  a 
difference  of  potential  be  ap- 
plied between  conductors  at- 
tached to  the  two,  we  have 
the  following  conditions : 

The  instrument  is  a  con- 
denser, the  double-ended  sec- 
tor, ftfi,  forming  one  coating, 
the  dielectric  being  air  and 
the  outer  coating  being  the 
stationary  sectors,  aa.  When 
the  difference  of  potential  is  applied  between  the  inner 
and  outer  coatings,  the  former,  being  movable,  tends  to 
rotate  with  a  force  proportional  to  the  potential  about 
its  axis,  e,  in  order  that  it  may  place  itself  in  a  posi- 
tion where  the  capacity  of  the  condenser  is  a  maximum ; 


FIG.  19. 


STANDARDS  OF  RESISTANCE.  31 

in  other  words,  to  turn  until  it  is  completely  enshrouded  by 
aa.  This  force  is  resisted  by  the  torsional  elasticity  of  the 
metallic  suspension  fiber,  e,  and  the  resulting  deflection  is 
therefore  a  measure  of  the  applied  voltage. 

Instruments  for  the  measurement  of  E.M.F.,  based  on  this 
principle,  are  called  electrostatic  voltmeters  or  electrometers. 
Although  they  are  in  somewhat  common  use  abroad  they  are 
not  as  well  known  or  as  much  relied  upon  in  this  country  as 
standards  for  the  measurement  of  potentials. 

The  deflectional  forces  are  small  as  compared  with  those 
existing  in  some  other  types  of  instruments,  so  it  is  necessary 
to  suspend  delicately  the  moving  element,  and  even  then  they 
cannot  be  used  for  the  measurement  of  very  low  potentials. 
On  the  other  hand,  they  are  entirely  independent  of  tempera- 
ture, can  be  used  on  either  direct  or  alternating  current,  are  not 
influenced  by  magnetic  fields,  consume  no  current,  and,  in  fact, 
with  the  exception  of  the  possibility  of  an  error  caused  by 
adjacent  electrostatic  influences  (from  which,  however,  it  is 
possible  to  shield  them  by  a  grounded  metallic  casing),  their 
deflections  with  a  given  potential  depend  only  on  their  geomet- 
rical dimensions  and  the  elasticity  of  the  suspending  fiber. 
The  latter  can  be  made  a  very  constant  and  reliable  quantity 
by  selecting  a  length  of  the  fiber  such  that  the  stress  in  it,  due 
to  its  being  twisted,  is  but  a  small  fraction  of  the  limit  of 
elasticity.  Electrostatic  voltmeters  may  therefore  be  made  as 
acceptably  reliable  standards. 

Where  the  voltages  to  be  measured  are  comparatively  low,  of, 
for  instance,  an  order  of  100  volts,  sufficient  deflectional  force 
is  obtained  by  superimposing  several  sets  of  charged  rotatable 
vanes  swinging  between  a  corresponding  number  of  stationary 
charged  plates.  Instruments  so  constructed  are  multicellular 
electrostatic  voltmeters,  and  one  of  them  of  a  commercial  type 
is  shown  in  Fig.  2.0,  this  being  an  illustration  of  the  Kelvin 
meter.  In  this,  voltage  is  indicated  by  a  needle  that  sweeps 
over  a  suitably  graduated  scale,  and  the  indications  are  damped 
by  a  disk  attached  to  the  movable  portion  and  moving  .'11  a 
vessel  containing  oil  that  is  inserted  in  the  lower  part  of  the 
instrument,  as  shown  by  the  partially  broken  away  part  in  the 
figure.  In  the  laboratory  standard  type  of  this  instrument,  a 
small  mirror  is  attached  to  the  moving  system,  and  by  means  of 


32       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

a  beam  of  light  thrown  on  it  and  reflected  to  a  fixed  scale,  the 
equivalent  of  a  very  long  needle  is  obtained,  which  enables  one  to 
read  the  indications  with  a  high  degree  of  accuracy.  The  Board 
of  Trade  standard  laboratory  in  London  has  a  set  of  electrostatic 
voltmeters  of  this  class,  one  of  which  is  shown  in  Fig.  21.  These 
have  no  numerically  divided  scales,  but  only  two  reference  lines, 
one  of  which  shows  the  position  of  the  moving  element  when 

no  current  is  applied,  and  the 
other  when  a  certain  potential, 
such  as  100,  500,  1000,  etc., 
volts,  is  applied.  In  the  illus- 
tration the  metallic  hood  cov- 
ering the  instrument  is  shown 
as  removed  and  placed  at  one 
side  of  the  apparatus?  To 
shield  against  foreign  electro- 
static charges  this  cover  when 
in  place  is  grounded.  The  in- 
dications of  this  instrument  also 
are  damped  by  means  of  an  oil 
cup.  It  is  claimed  that  the 
electrostatic  voltmeters  at  the 
Board  of  Trade  laboratory  give 
indications  that  are  accurate 
within  one  part  in  3000. 

Volt  Balances. 

From  Ohm's  law,  the  current 
passing  through  a  circuit  is  di- 
rectly proportional  to  the  voltage 
applied,  if  the  resistance  of  the 
circuit  be  kept  constant.  If, 
therefore,  we  take  any  current-consuming  instrument  that  would 
ordinarily  indicate  amperes,  having  a  resistance  sufficiently  high 
so  that  the  current  drawn  would  not  pull  down  the  E.M.F.  of 
the  source  to  be  measured,  or  to  heat  the  conductors  forming  the 
instrument  sufficiently  to  alter  its  resistance,  the  indications  of 
the  instrument  will  vary  in  proportion  to  the  applied  voltage, 
and  the  scale  may  be  divided  to  read  volts  instead  of  amperes. 
The  Kelvin  Centiampere  Balance,  designed  to  measure  cur- 


STANDARDS  OF   RESISTANCE.  33 

rents  varying  in  value  from  .01  to  1  ampere,  is  frequently 
used  as  a  standard  voltmeter  on  this  principle,  by  inserting 
in  series  with  it  a  properly  adjusted  known  high  resistance, 
that  may  be  obtained  from  the  makers.  The  value  of  the  re- 
sistance is  made  such  that  the  values  indicated  by  the  movable 
rider  on  the  balance  indicate  volts  directly,  or  else  some  simple 
multiple,  such  as  one  half,  one  tenth,  etc.,  of  the  numerals  in 
volts.  The  measurement  of  potentials  in  this  way  depends,  as 
above  stated,  on  the  assumption  that  the  resistance  of  the  in- 
strument remains  constant  during  the  test.  As  copper,  the 
material  of  which  the  wire  coils  of  the  balance  are  formed,  has 
a  resistance  that  varies  quite  markedly  with  a  change  in  tem- 


21. 


perature,  it  is  necessary,  where  accurate  results  are  required,  to 
correct  for  such  changes  of  temperature.  For  this  purpose, 
the  temperature  is  observed  by  a  thermometer,  which  is  inserted 
as  close  as  possible  to  the  coils. 

STANDARDS    OF    CAPACITY. 

As  has  been  stated  on  page  4,  capacity  is  the  property  by 
virtue  of  which  two  electrical  conductors,  insulated  from  each 
other,  will  store  up  a  quantity  of  electricity,  if  a  difference  of 
potential  be  applied  to  them.  The  amount  of  charge  depends 
on  the  area  of  the  opposing  surfaces,  on  the  distance  between 


34        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

them,  and  the  nature  of  the  intervening  medium ;  namely, 
whether  this  be  air,  glass,  mica,  or  paper,  or  any  other  sub- 
stance. Such  a  device  for  storing  up  an  electric  charge  is  called 
a  "  condenser." 

Condensers  that  are  to  be  used  as  standards  are  often  con- 
structed so  that  the  dielectric  intervening  between  adjacent  sides 
is  air,  and  the  spacings  between  the  plates  are  kept  constant 
by  a  rigid  mechanical  construction.  The  capacity  of  such 
standards  is  determined  by  measurements  involving  the  ele- 
ments of  current  strength  and  time  in  one  of  the  ways  de- 
scribed in  Chapter  VIII,  and  may  then  be  used  for  purposes  of 
comparison.  The  construction  of  the  standard  Kelvin  air  con- 
denser is  shown  in  Fig.  22. 

Condensers  in  which  air  is  the  dielectric  are  bulky  because 
of  the  mechanical  construction,  and  heavy  because  the  plates 


FIG.  22. 


must  be  made  thick  enough  to  support  themselves.  It  is  possi- 
ble to  make  a  form  which  is  as  satisfactory  as  regards  perma- 
nence, and  far  lighter  and  more  compact,  by  using  mica  as  the 
dielectric.  The  ordinary  construction  in  such  cases  is  to  make 
the  conductors  of  strips  of  tinfoil  with  mica  plates  intervening. 
However,  unless  the  pressure  holding  this  aggregation  of  mica 
and  tinfoil  assembled  together  is  kept  rigorously  constant, 
the  capacity  will  vary,  due  to  the  fact  that  the  dielectric 
between  the  adjacent  tinfoil  coatings  is  a  varying  thickness 
of  air  and  mica  instead  of  a  constant  thickness  of  mica  alone. 
To  minimize  trouble  OR  this  score,  the  condensers  are  usually 
well  soaked  in  paraffine,  which  effectually  prevents  the  entrance 
of  air  and  makes  a  more  or  less  solid  mass.  A  much  more 
satisfactory  expedient,  however,  is  that  used  by  Mr.  Hamilton, 
in  which  a  thin  film  of  silver  is  chemically  precipitated  upon, 


STANDARDS  OF  RESISTANCE.  35 

and  strongly  adheres  to  the  mica  plates.  The  coatings  on  each 
side  of  a  plate,  with  the  intervening  mica,  form  a  condenser 
of  small  capacity.  By  assembling  a  sufficient  number  of  these 
small  condensers  in  one  case,  and  interconnecting  them,  a  con- 
denser of  any  required  capacity  may  be  formed.  The  final  ad- 
justment is  made  by  utilizing  the  fact  that  the  sheets  of  mica 
vary  in  thickness,  and  consequently  the  capacities  of  the  differ- 
ent elements  are  different,  together  with  the  principle  that 
series  connection  of  two  or  more  elements  reduces  the  capacity 
of  the  whole.  Having  some  extra  elements,  a  few  substitutions 
of  thick  for  thin  ones,  or  vice  versa,  will  bring  the  capacity  at 
least  pretty  closely  to  the  desired  magnitude,  and  if  the  exact 
value  cannot  be  reached  in  this  manner,  it  may  be  reached 
either  by  connecting  some  elements  in  series  or  by  scraping 
away  a  part  of  the  coating  from  some  of  the  plates.  Such  con- 
densers are  fully  as  reliable  as  the  air  form,  and  may  be  used  as 
standards  with  equal  confidence.  It  is  stated  that  their  accuracy 
will  change  less  than  one  part  in  one  thousand,  even  after  taking 
apart  and  reassembling. 

Condensers  have  temperature  coefficients,  that  is  to  say,  their 
capacity  varies  to  some  extent  with  changes  in  temperature,  so 
that  in  comparison  methods  of  measurement,  the  temperatures 
of  the  standard,  and  unknown  condensers  must  be  taken  into 
consideration. 

STANDARDS    OF    INDUCTANCE. 

As  in  the  case  of  capacity,  inductance  is  a  property  of  an 
electrical  circuit,  which  is  defined  in  terms  of  more  funda- 
mental units,  namely,  the  volt,  the  ampere,  and  the  second,  and 
standards  are  prepared  by  making  up  a  circuit  having  induc- 
tance, measuring  that  inductance  by  one  of  the  primary  methods 
described  in  Chapter  IX,  and  afterwards,  if  desired,  using  it  for 
comparison  purposes  when  making  measurements  involving  the 
use  of  a  comparison  standard.  According  to  the  definition  of 
inductance,  this  property  depends  on  having  the  magnetic  lines 
of  force  which  surround  a  current-carrying  conductor  cut 
another  conductor  or  another  portion  of  the  same  one.  A 
standard  that  is  economical  of  manufacture,  compact,  and  effi- 
cient must  therefore  have  its  elements  arranged  so  that  this 
cutting  action  is  a  maximum.  This  condition  will  exist  when  a 


36        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


conductor  is  wound  up  into  a  form  of  coil,  for  in  that  case  (see 
Fig.  23,  which  shows  in  section  a  coil  of  five  turns  in  which  the 
lines  of  force  surrounding  one  portion  of  the  first  turn  are  de- 
picted), the  lines  of  force  surrounding  each  conductor  will  evi- 
dently, when  generated,  cut  all  of  the  other  conductors,  and  as 
inductance  is  manifested  only  when  current  strength  is  chang- 
ing, tliis  cutting  will  generate 
in  the  portions  cut  a  progres- 
sive and  continuously  opposing 
E.M.F.  If  we  afford  a  path 
of  less  resistance  to  the  flow 
of  the  lines  of  force  than  that 
offered  by  air,  the  maximum 
effect  is  evidently  increased, 
that  is,  a  given  coil  has  more 
inductance  when  a  good  con- 
ductor of  magnetic  flux,  such 
encloses  the  coil.  The  addi- 
inductance  is,  however,  not 


FIG.  23. 


as  iron,  wholly  or  partially 
tion  of  iron  to  increase  the 
permissible  in  a  standard,  for  two  reasons.  First,  the  perme- 
ability of  iron  is  not  a  constant  quantity,  but  varies  with  the 
density  of  the  magnetic  induction.  Consequently,  the  induc- 
tance, which  is  proportional  to  the  total  magnetic  flux 
divided  by  the  current,  is  not  a  con- 
stant, but  is  different  for  each  current 
strength.  This  alone  would  be  fatal 
in  a  standard,  but  there  is  a  second 
property  of  iron,  called  "hysteresis," 
or  magnetic  retentiveness,  owing  to 
which  the  magnetic  flux  is  not  always 
the  sams  for  the  same  current,  but 
depends,  in  part,  on  the  preceding 
magnetic  condition  of  the  iron,  which 
furnishes  just  as  potent  a  reason  why 
the  use  of  iron  to  increase  the  induc- 
tance of  a  standard  is  not  permissible. 


FIG.  24. 


If  in  Fig.  23  instead  of  having  one  coil  of  five  turns  this 
were  divided  into  two  sections,  one  of  three  and  the  other  of  two 
turns,  having  the  relative  positions  shown,  the  inductance  of 
the  whole  would,  of  course,  be  the  same.  If,  however,  it  were 


STANDARDS  OF  RESISTANCE.  37 

arranged  so  that  one  of  the  sections  could  be  displaced  relative 
to  the  other,  the  action  of  one  part  on  the  other  would  be  in  some 
manner  related  to  the  displacement.  This  fact  is  utilized  in  the 
inductance  standard  known  as  the  "  Ayrton  and  Perry,"  one  of 
which  is  shown  in  Fig.  24.  This  consists  of  an  outer  stationary 
coil  of  wire  within  which  there  is  the  other  coil,  and  the  angle 
that  the  latter  makes  with  the  axis  of  the  former  may  be  varied 
by  manipulating  the  knurled  button.  The  inductance  is  at  a 
maximum  when  the  planes  of  the  two  coils  are  parallel,  as  then 
the  mutual  interaction  of  the  two  is  greatest ;  and  at  a  minimum 
when  the  planes  of  the  two  coils  are  at  right  angles,  for  analo- 
gous reasons.  A  dial-shaped  scale  is  provided  over  which  plays 
a  pointer  attached  to  the  axis  of  the  movable  element,  and  by 
calibration  in  comparison  with  other  standards  the  scale  may  be 
divided  off  to  show  directly  the  commercial  units  of  induc- 
tance (millihenrys)  that  are  offered  by  each  coil  position. 


CHAPTER   III. 

GALVANOMETERS . 

THE  electric  current  is  imponderable  and  cannot,  therefore,  be 
compared  as  to  weight  or  dimensions  with  a  standard,  as  pon- 
derable masses  are,  but  must  be  compared  with  other  currents 
by  means  of  some  effect  or  property  of  the  current  which  is  a 
measurable  magnitude. 

An  electric  current  may  manifest  itself  in  several  ways.  It 
may  effect  chemical  composition  or  decomposition,  as  in  the  case 
of  the  silver  voltameter  before  mentioned ;  its  action  may  be 
electromagnetic,  in  that  the  magnetic  field  surrounding  the  con- 
ductor carrying  the  current  will  influence  an  adjacent  magnet 
and  tend  to  displace  it,  as  in  an  ordinary  polarized  telegraph  re- 
lay ;  its  action  may  be  electrostatic,  as  in  the  case  of  pith  balls, 
which  are  attracted  to  or  repelled  from  an  electrified  glass  rod  ; 
or  it  may  be  thermal,  as  in  the  case  where  a  current  passing 
through  a  conductor  causes  the  temperature  of  the  latter  to  rise. 

Instruments  for  at  least  detecting  the  presence  and  preferably 
for  measuring  the  magnitude  of  one  or  more  of  these  actions  are 
necessary  if  we  are  to  have  a  means  of  comparing  current 
strengths.  Such  instruments  have  the  generic  name  of  "gal- 
vanometers." 

Galvanometers  based  on  the  chemical  action  of  an  electric 
current  are  in  very  limited  use  and  need  not  be  enlarged  upon 
here.  The  great  majority  of  commercially  available  forms 
utilize  the  electromagnetic  manifestations  of  current  and  may, 
generally  speaking,  be  divided  into  two  classes  ;  first,  the  moving 
magnet  class  in  which  a  movable  magnet  is  influenced  by  the 
current  flowing  in  a  fixed  conductor,  and  the  second,  the  mov- 
ing coil  class,  in  which  the  current  to  be  measured,  or  a  known 
portion  thereof,  is  passed  through  a  movable  conductor,  usually 
in  the  shape  of  a  coil,  located  within  the  influence  of  a  magnetic 
field  which  may  be  either  that  of  a  permanent  magnet,  or  that  of 
a  current-carrying  conductor. 

38 


GALVANOMETERS.  39 

In  either  case  one  of  the  elements  is  fixed  and  the  other  free 
to  move  against  a  measurable  restraining  force,  and  the  extent 
of  the  movement  of  the  latter  as  indicated  by  suitable  means  is 
a  measure  of  current  strength.  With  galvanometers  of  the  first 
class,  those  in  which  there  is  a  movable  magnet  and  a  fixed  coil, 
the  former  is  almost  invariably  a  magnetized  steel  needle  or 
group  of  needles,  usually  straight,  but  sometimes  bent  double 
about  their  centers  and  taking  on  the  form  of  a  slotted  bell 
(see  Fig.  25).  In  all  these  instruments  the  movable  needle  is 
suspended  from  a  fiber  that  offers  the  minimum  possible  resist- 
ance to  its  turning,  the  measurable  restraining  force  being  that 
furnished  by.  an  external  magnetic  field,  sometimes  that  of  the 
earth  itself,  and  sometimes  one  furnished  by  adjacent  magnets 
whose  positions  and  distances  are  adjustable.  In  high  sensibil- 
ity galvanometers  the  forces  involved  are  so  minute  that 
the  delicacy  of  the  suspension  becomes  a  most  impor- 
tant item.  It  is  altogether  out  of  the  question  to  use  a 
pointed  hardened  steel  pivot  support  engaging  in  a 
jewel-bearing,  as  the  friction  between  the  two  would  be 
commensurate  with  the  deflectional  forces  and  large 
errors  thus  introduced.  Great  delicacy  is  obtained  by 
supporting  the  movable  needle  on  a  fiber  of  cocoon  silk 
of  considerable  length.  Even  this,  however,  is  inferior 
to  a  suspension  formed  of  a  very  fine  filament  of  quartz. 
Such  may  be  constructed  by  heating  a  short  quartz  rod  to  N  s 
incandescence  in  an  oxyhydrogen  blowpipe  flame,  and 
having  one  end  rigidly  secured  to  a  fixed  block,  suddenly  re- 
tracting the  other  end,  usually  by  having  it  fastened  to  a 
miniature  form  of  crossbow  in  which,  when  the  trigger  is  re- 
leased, the  end  is  shot  forward  with  great  velocity.  The  fila- 
ment is  in  this  manner  drawn  out  to  a  very  small  diameter 
before  rupture. 

As  galvanometer  sensibility  may  be  increased  either  by 
decreasing  the  amount  of  restraining  force  for  a  given  deflec- 
tional angle  or  by  increasing  the  number  of  ampere  turns  sur- 
rounding the  needle,  and  as  the  latter  is,  from  motives  of 
efficiency,  made  as  great  as  possible  in  the  beginning,  the  sensi- 
bility can  evidently  be  further  increased  only  by  decreasing  the 
strength  of  the  controlling  field.  If  this  is  the  field  due  to  the 
earth's  magnetism,  its  directive  force  may  be  diminished  or,  in 


40          ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

fact,  completely  annuled  or  reversed  by  placing  near  to  the  gal- 
vanometer a  magnetized  body  which  sets  up  a  flux  opposite  in 
direction  to  that  of  the  earth's  field.  If  the  two  were  exactly 
alike  and  opposite  there  would  evidently  be  no  restraining 
force  except  the  negligible  one  of  the  torsional  elasticity  of  the 
fiber,  and  the  needle,  influenced  by  the  current  passed  through 
the  coil  surrounding  it,  would  assume  a  position  practically  at 
right  angles  to  the  plane  of  the  coil  with  any  current  strength, 
no  matter  how  small,  and  thus  fail  to  act  as  an  index  of  current 
strength. 

When,  however,  one  or  the  other  of  the  magnetic  forces  pre- 
ponderates, there  is  a  directive  force  which  tends  to  retain  the 
needle  in  the  zero  position.  The  resultant  between  this  and  the 
directive  force  of  the  field,  due  to  the  flow  of  the  current,  deter- 
mines the  position  of  the  needle.  Theoretically,  therefore,  all 
that  is  necessary  to  obtain  almost  infinite  sensibility  is  an  almost 
infinitesimal  difference  between  the  field  due  to  the  directive 
magnet  and  that  of  the  earth,  but  this  is  based  on  the  assumption 
that  the  suspension  device  is  f  rictionless  and  absolutely  flexible. 
As  a  matter  of  fact,  the  suspension  fiber  must  be  of  sufficient 
size  to  have  the  necessary  strength  for  the  mechanical  support 
of  the  needle,  and  the  resultant  torsional  rigidity  or  inelastic 
resistance  to  torsion  is  of  such  magnitude  that  the  directive 
force  must  be  made  quite  large  in  order  to  render  it  negligible. 
In  practice,  to  obtain  maximum  sensibility  with  a  moving  mag-  ; 
net  galvanometer,  a  current  is  passed  through  it  to  cause  a 
deflection,  preferably  the  full  scale  in  amplitude,  and  the  current 
then  cut  off  to  see  whether  the  magnet  returns  to  its  initial 
position.  If  so,  the  control  magnet  is  approached  a  little  closer. 
The  operation  is  repeated  until,  on  opening  the  circuit,  the  in- 
dex showing  the  movement  of  the  needle  no  longer  comes  back  to 
its  starting  point.  It  is  then  evident  that  the  controlling  force 
is  too  weak,  so  the  magnet  must  be  moved  away  again,  just  far 
enough  to  insure  the  return  of  the  index  to  zero  every  time  the 
current  is  cut  off. 

Moving  coil  instruments  may  be  conveniently  divided  into 
two  subclasses  namely,  those  in  which  the  coil  moves  because 
of  the  reaction  between  the  current  through  it  and  a  powerful 
stationary  permanent  magnet,  and  the  class  in  which  the  reac- 
tion is  between  the  current-carrying  coil  and  stationary  coils 


GALVANOMETERS. 


41 


likewise  traversed  by  currents  setting  up  lines  of  force  therein. 
In  movable  coil  galvanometers,  silk  and  quartz  suspension  fibers 
are  inadmissible  inasmuch  as  the  suspensions  are  used  as  a  means 
of  conducting  the  current  to  be  measured  to  the  movable  coil. 
What  is  ordinarily  used,  therefore,  is  a  narrow  and  extremely 
thin  strip  of  phosphor  bronze  made  by  rolling  down  by  successive 
passages  through  jeweler's  rolls  a  small  diameter  phosphor 
bronze  wire.  This  is,  of  course,  a  conductor,  and  if  the  movable 
element  be  suspended  above  by  one  such  conductor  and  steadied 
below  by  another,  both  being  held  taut,  they  evidently  perform 
the  double  function  of  conductors  and  opposing  springs. 


8 


FIG.  26. 

It  is  also  possible  to  support  the  movable  element  by  two 
such  metallic  strips,  both  supporting  it  from  above.  Another 
form  of  construction  is  shown  in  5,  Fig.  26.  In  this  construc- 
tion the  metallic  strip  is  coiled  helically,  and  when  the  movable 
element  deflects,  the  ordinary  spring  action  of  a  helically  coiled 
wire  is  brought  into  play  in  place  of  its  torsional  elasticity,  as 
in  the  straight  form  shown  in  a  of  the  same  figure.  At  c  is 
shown  the  movable  coil  suspended  from  above  by  two  conduc- 
tors, as  already  mentioned.  In  the  forms  a  and  b  it  is  evidently 
possible  to  substitute  for  the  lower  metallic  spring  strip  a  very 
flexible  current-carrying  strip,  which  offers  no  appreciable 


42          ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

resistance  to  motion  and  at  the  same  time  serves  as  a  con- 
ductor. Such  flexible  connections  are  usually  made  of  soft 
annealed  pure  silver  wires.  In  the  form  of  suspension  shown 
in  a,  b,  and  d,  the  resistance  to  turning  offered  by  the  suspen- 
sions can  be  altered  only  by  changing  them.  In  the  form 
shown  in  c,  however,  if  the  distance  between  the  two  suspensions 
at  their  upper  end  is  increased,  a  greater  effort  will  evidently 
be  required  to  produce  the  same  angular  displacement.  This 
bifilar  suspension,  as  it  is  called,  is  convenient  in  some  respects 
but  not  in  very  common  use  in  this  country. 

The  means  employed  to  indicate  the  extent  of  the  movement 
of  the  swinging  member  of    a  galvanometer  is  also  of    much 
importance.     As  the  latter  usually  rotates  about  an  axis,  it  is 
evident  that  any  index  actuated   by  it  will  have  a  greater  linear 
displacement  over  a  fixed  scale  for  a  given   angular  displace- 
ment, the  further  the  scale  and   the   marking  extremity  of  the 
index  are  from  the  axis.     This  at  once   suggests  the  use  of  a 
very  long  hand  or  pointer,  but  this  is  objectionable   because  of 
its  Aveight,  which  not  only  adds  very  considerably  to  the  inertia 
of  the  moving  system,  and  so  renders   its  response  to  current 
changes  slow,  but  necessitates  stronger  suspensions   to  support 
it,  which  suspensions  are,  of  course,  more  rigid,  and  therefore 
decrease  the  sensibility  of  the  galvanometer.      This  difficulty  is 
surmounted    by   using  in    place   of   the    ponderable    pointer  a 
beam  of  light  reflected  from  a  mirror   carried  on  the  movable 
part.     This  arrangement  may  assume  one   of    two  forms.     In 
the  first,  a  telescope  is  used,  arranged  as  shown  in  Fig.  27,  where 
ab  is  the  mirror  carried  by  the  moving  system,  T  the  telescope, 
and  SS  the  scale.     The  telescope  is  provided  with  a  stretched 
hair,  W,  as  in  a  surveyor's  transit,  which  serves  as  a  reference 
line  for  the  position  of   the  image  of  the  scale  markings  as  seen 
through  the  telescope  reflected  from  the  mirror.     If  the  moving 
system,  and  therefore  the  mirror,  ab,  attached  thereto,  moves 
through  an  angle  a,  the  angle  between  the  axis  of  the  telescope 
and  the  axis  of  the  ray  of  light  reflected  from  the  mirror  is 
evidently  2a,  the   apparent  deflection  being  thus  doubled.     In 
order  that  there  may  be  a  minimum  loss  in  illumination  due  'to 
the  absorption  by  the  lenses  in  the  telescope,  the  latter  is  usu- 
ally made  of  the  astronomical  type,  presenting  to  the  eye  an 
image    that  is  reversed  and  inverted  (that  is   to  say,   turned 


GALVANOMETERS. 


43 


through  an  angle  of  180°),  while  the  mirror  reverses  in  the  sense 
in  which  ordinary  printing  type  are  reversed.  It  follows,  there- 
fore, that  a  scale,  the  reflection  of  which  in  a  mirror  is  to  be 
observed,  must  have  its  numerals  reversed,  like  ordinary  printing 
type,  and  if  they  are  to  be  viewed  through  an  astronomical  tele- 
scope, the  scale  must  be  placed  in  the  instrument  in  an  inverted 
position,  so  that  the  numerals  appear  to  the  direct  vision 
thus  J  $•  '3  ?  3.  If  an  erecting  telescope  or  simple  slot  be 
used,  the  scale  is  placed  in  the  instrument  in  an  erect  position, 
so  that  the  numerals  appear  to  direct  vision  thus,  Q  £  5  S  I  • 
In  both  cases  the  numerals  will  appear  in  their  normal  as- 
pect, 1  2  3  4  5,  when  seen  while  making  a  scale  reading. 


B 


FIG.  27. 


On  looking  through  the  telescope  when  current  is  applied,  the 
whole  scale  swings  across  the  field  or  vision,  the  reference 
line  made  by  the  cross-hair  remaining  fixed.  It  is  of  course 
possible  to  use  instead  of  a  telescope  a  small  diameter  hole  or  a 
long  narrow  slot,  but  this  calls  for  better  illumination,  in  order 
to  make  the  scale  markings  visible,  and  for  good  eyesight. 

This  first  type  of  movement-indicating  device  enables  one  to 
make  very  close  readings,  as  the  cross-hair  furnishes  a  sharply 
defined  reference  line.  On  the  other  hand,  it  is  trying  to  the 
eyes,  only  one  of  which  can  be  used  at  a  time.  It  is  also 
inconvenient  in  that  only  one  party  can  observe  the  indications 
at  a  given  time. 


- 


© 


44        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

In  the  second  plan  an  actual  luminous  beam  is  used.  Re- 
ferring to  Fig.  28,  L  is  a  source  of  light  arranged  with  a  hood, 
or  otherwise,  so  that  it  sends  out  only  a  long  narrow  beam  which 
is  reflected  by  a  mirror  or  prism  at  M,  concentrated  by  the  lens, 
Z,  and  thrown  on  the  galvanometer  mirror,  ab.  The  latter 
is  made  concave  to  keep  the  beam  concentrated,  and  the  light  is 
thrown  from  there  onto  a  fixed  scale,  SS,  usually  made  of 
ground  glass  and  having  pasted  thereon  an  opaque  scale  divided 
into  millimeters,  or  other  convenient  units.  This  beam  falling 
upon  the  ground  glass  scale  plate  makes  a  luminous  line  whose 
position  relative  to  the  opaque  scale  can  usually  be  read  with 
great  ease.  Readings  can  be  made  to  a  greater  degree  of 
accuracy  in  the  telescope  pattern  instrument  because  the  lu- 
minous band  has  an  edge  such 
that  it  is  difficult  to  say  just 
where  it  leaves  off,  but  chi  the 
f  other  hand,  the  second  form 
is  advantageous  because  sev- 
eral observers  may  simultane- 
J/  ously  note  the  swing,  and  it 
is  much  easier  on  the  eyes. 
The  only  remaining  argument 
for  the  first  form  is  that  it  can 
be  read  in  the  daylight,  the 
brighter  the  better,  whereas 
8  the  latter  needs  darkness,  if 

it  is  to  be  shown  to  advantage. 

Because  the  scale,  SS,  Figs.  27  and  28,  is  straight  instead  of 
being  bent  into  the  form  of  a  circle  arc  about  the  mirror  as  a 
center,  the  linear  displacements  shown  thereon  are  proportionate, 
not  to  the  angle  through  which  the  movable  element  has  swung, 
but  to  the  tangent  of  twice  that  angle.  Where  the  angular 
deflections  are  but  small,  the  difference  between  the  numerical 
value  of  an  angle  and  its  tangent  is  negligible  and  the  linear 
displacement  on  the  scale  may  be  taken  as  proportionate  to  the 
angular  deflection.  However,  when  measuring  large  deflections, 
and  where  accurate  results  are  required,  the  angles  should 
be  calculated  from  the  above  relation  between  them  and  the 
linear  motion.  The  following  table  computed  by  Dr.  Kennelly 
gives  the  correction  factors  to  be  applied  with  different  distances 
between  the  scale  and  mirror  and  for  varying  deflections : 

J 


GALVANOMETERS. 


45 


TABLE  II. 

Reflecting  Galvanometer  Scale  Errors. 

(A.  E.  KEXXELLY.) 
(These  corrections  are  to  be  subtracted  from  the  observed  deflections.) 


Scale 
Distance 

1000 

1100 

1200 

1300 

1400 

1500 

1600 

1700 

1800 

1900 

2000 

50 

0.05 

0.05 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

0. 

60 

0.05 

0.05 

0.05 

0.05 

0.05 

0. 

0. 

0. 

0. 

0. 

0. 

70 

0.1 

0.05 

0.05 

0.05 

0.05 

0.05 

0.05 

0.05 

0.05 

0.05 

0. 

80 

0.15 

0.1 

0.1 

0.1 

0.05 

0.05 

0.05 

0.05 

0.05 

0.05 

0.05 

90 

0.2 

0.15 

0.15 

0.1 

0.1 

0.1 

0.05 

0.05 

0.05 

0.05 

0.05 

100 

0.25 

0.2 

0.2 

0.15 

0.15 

0.1 

0.1 

0.1 

0.1 

0.05 

0.05 

110 

0.35 

0.25 

0.25 

0.2 

0.2 

0.15 

0.15 

0.1 

0.1 

0.1 

0.1 

120 

0.45 

0.35 

0.3 

0.25 

0.25 

0.2 

0  15 

0.15 

0.15 

0.1 

0.1 

130 

0.55 

0.45 

0.4 

0.3 

0.3 

0.25 

0.2 

0.2 

0.15 

0.15 

0.15 

140 

0  7 

0.55 

0.5 

0.4 

0.35 

0.3 

0.27, 

0.25 

0.2 

0.2 

0.15 

150 

0.85 

0.7 

0.6 

0.5 

0.4 

0.35 

0.35 

0.3 

0.25 

0.25 

0.2 

160 

1.0 

0.85 

0.7 

0.6 

0.5 

0.45 

0.4 

0.35 

0.3 

0.3 

0.25 

170 

1.2 

1.0 

0.85 

0.7 

0.6 

0.55 

0.5 

0.45 

0.4 

0.35 

0.3 

180 

1.4 

1.2 

1.0 

0.85 

0.7 

0.65 

0.55 

0.5 

0.45 

0.4 

0.35 

190 

1.65 

1.4 

1.2 

1.0 

0.85 

0  75 

0.65 

0.6 

0.55 

0.5 

0.45 

200 

1.95 

1.65 

14 

1.15 

1.0 

0.9 

0.8 

0.7 

0.6 

0.55 

0.5 

210 

2.25 

1.9 

1.6 

1.35 

1.15 

1.05 

0.9 

0.8 

0.7 

0.65 

0.6 

220 

2.6 

2.15 

1.8 

1.55 

1.3 

1.2 

1.05 

0.9 

0.8 

0.75 

0.65 

230 

2.95 

2.45 

2.05 

1.75 

1.5 

1.35 

12 

1.05 

0.95 

0.85 

0.75 

%        240 

3.3 

2.8 

2.35 

2.0 

1  .75 

1.5 

1.35 

1.2 

1.05 

0.95 

0.85 

o         250 

3.75 

3.15 

2.65 

2.25 

1  95 

1.7 

1.5 

1.35 

1.2 

1.05 

1.0 

H 

g        260 

4.25 

3.5 

3.0 

2.55 

2  2 

1.9 

1.7 

1.5 

1.35 

1.2 

1.10 

3         270 

4.75 

3.95 

3.35 

2.85 

2.45 

2.15 

1.9 

1.7 

1.5 

1.35 

1.25 

^         280 

5.3 

4.4 

3.7 

3.15 

2.75 

2.4 

2.1 

1.9 

1.65 

1.5 

1.35 

0 

a         290 

5.85 

4.85 

4.1 

3.5 

3.05 

2.65 

2.35 

2.1 

1.85 

1.65 

1.5 

-         300 

6.45 

5.35 

4.5 

3.9 

3.35 

2.95 

2.6 

2.3 

2.05 

1.85 

1.7 

«         310 

7.1 

5.9 

5.0 

4.3 

3.7 

3.25 

2.85 

2.5 

2.25 

2.05 

1.85 

I        320 

7.8 

6.5 

5.5 

4.7 

4.05 

3.55 

3.15 

2.75 

2.45 

2.25 

2.05 

§        330 

8.5 

7.1 

6.0_ 

5.15 

4.45 

3.9 

3.45 

3.05 

2.7 

2.45 

2.2 

340 

9.3 

7.75 

6.55 

5.6 

4.85 

4.25 

3.75 

3.35 

2.95 

2.65 

2.4 

350 

10.1 

8.4 

7.15 

6.1 

5.3 

4.6 

4.1 

3.65 

3.25 

2.9 

2.6 

360 

10.95 

9.15 

7.75 

6.65 

5.75 

5.0 

4.45 

3.95 

3.55 

3.15 

2.85 

370 

11.85 

9.9 

8.4 

7.2 

6.2 

5.45 

4.8 

4.3 

3.85 

3.40 

3.1 

380 

12.8 

10.7 

9.05 

7.8 

6.7 

5.9 

5.2 

4.65 

4.15 

3.7 

335 

390 

13.8 

11.5 

9.75 

8.4 

7.25 

6.35 

5.6 

5.0 

4.45 

4.0 

3.6 

400 

14.85 

12.4 

10.5 

9.05 

7.85 

6.85 

6.05 

5.35 

4.80 

4.3 

3.9 

410 

15.9 

13.3 

11.3 

9.7 

8.4 

7.4 

6.5 

5.75 

5.2 

4.65 

4.2 

420 

17.05 

14.25 

12.1 

10.4 

9.05 

7.95 

7.0 

6.2 

5.55 

5.0 

4.5 

430 

18.2 

15.25 

1295 

11.15 

9.7 

8.5 

75 

6.65 

5.95 

5.35 

4.85 

440 

19.45 

16.3 

13.85 

11  9 

10.35 

9.05 

8.0 

7.1 

6.35 

5.75 

5.2 

450 

20.7 

17.35 

14.75 

12.7 

11.05 

9.7 

8.55 

7.6 

6.8 

6.15 

5.R5 

460 

22.05 

18.5 

15.75 

13.5 

11.8 

10.35 

9.1 

8.1 

7.25 

6.55 

5.i; 

470 

23.45 

19.65 

16.8 

14.4 

12.55 

11.0 

9.7 

8.65 

7.75 

6.95 

6.3 

480 

24.85 

20.9 

17.85 

15  3 

13.3 

11.7 

10.35 

9.2 

8.25 

7.4 

6.7 

490 

26.35 

22.2 

18.9 

16.25 

14.15 

12.4 

110 

9.75 

8.75 

7.85 

7.1 

500 

27.9 

23^55 

19.95 

17.2 

15.0 

13.2 

11.65 

10.35 

9.3 

8.35 

7.55 

46        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

We  will  now  proceed  to  consider  commercial  forms  of 
galvanometers. 

MOVABLE    COIL    OR    D'ARSONVAL    TYPE. 

Galvanometers  with  movable  coils  through  which  the  current 
to  be  measured  is  passed,  and  in  which  the  coils  rotate  in  the  field 
furnished  by  a  powerful  permanent  magnet,  are  said  to  be  of  the 
D'Arsonval  type.  An  early  form  of  the  D'Arsonval  galvanom- 
eter is  shown  in  Fig.  29.  The  magnet  furnishing  the  field  is  of 
the  compound  pattern  made  of  several  U-shaped  permanent 
magnets  bolted  together  and  secured  vertically  to  the  base  of 


FIG.  29. 


the  apparatus.  In  the  gap,  between  the  legs  of  the  magnet  is 
placed  a  cylinder  of  soft  iron  supported  from  the  rear,  which 
decreases  the  reluctance  of  the  magnetic  circuit  and  makes  the 
density  in  the  air  gap  between  its  face  and  the  magnet  faces  a 
maximum,  the  resultant  powerful  field  giving  a  maximum  re- 
action for  a  given  current  strength.  Surrounding  the  central 


GALVANOMETERS.  47 

cylindrical  core,  there  is  a  rectangular  loop  made  of  many  turns 
of  wire  supported  from  above,  coaxially  with  the  cylinder  by 
means  of  a  fine  silver  or  alloy  strip,  as  already  mentioned.  The 
lower  side  of  the  loop  is  steadied  by  a  similar  strip,  which  in 
turn  is  secured  at  its  end  to  a  stiff  flat  brass  spring.  The  elas- 
ticity of  this  spring  keeps  the  strips  taut  and  the  coil  perfectly 
centered.  The  tension  on  the  strips  may  be  varied  by  means  of 
a  suitable  thumb-screw,  as  shown.  A  small  circular  mirror  hav- 
ing either  a  plane  or  a  concave  surface,  according  to  the  method 
to  be  employed  in  reading  the  indications  of  the  instrument,  is 
cemented  to  an  upright  rod  firmly  attached  to  the  coil.  The 
current  to  be  measured  is  led  into  the  coil  through  the  upper 
metallic  suspension,  through  the  several  turns  of  wire  com- 
posing the  coil,  and  out  again  through  the  lower  strip  and  flat 
spring  attached  thereto.  The  whole  apparatus  is  kept  covered 
by  a  glass  bell  to  prevent  disturbance  by  air  currents,  and  .in  the 
bell  jar  there  is  provided,  a  window  of 
very  thin  clear  glass,  such  as  used  for 
microscope  slides,  through  which  the 
beam  of  light  may  pass  without  distor- 
tion. 

It  will  be  observed  (see  Fig.  30  show- 
ing diagrammatically  a  plan  view  of  a 

suspended  coil  galvanometer)  that  the  D'Arsonval  instrument  is 
simply  a  miniature  motor,  with  fixed  permanent  magnets  for 
furnishing  the  field  flux,  the  movable  coil,  e,  forming  the 
armature  winding,  and  the  fixed  cylinder,  c,  the  armature  core. 
The  force  with  which  the  coil  tends  to  place  itself  at  right 
angles  to  the  position  shown  is  thus  dependent  upon  ex- 
actly the  same  elements  that  determine  the  torque  of  a  motor, 
that  is  to  say,  the  strength  of  the  field,  the  number  of  turns  of 
wire  in  the  coil,  and  the  strength  of  the  current  flowing  through 
that  coil.  High  sensibility  may  therefore  be  obtained  by  using 
the  most  powerful  possible  permanent  magnets,  and  by  the  em- 
ployment of  the  maximum  number  of  turns  of  fine  insulated 
wire  in  the  loop,  at  the  same  time  making  the  restraining  frrce 
of  the  elastic  strips  as  small  as  possible.  If  instead  of  simply 
winding  the  wire  into  a  rectangular  coil,  it  is  wound  up  on  a 
metallic  frame,  preferably  copper  or  aluminum,  because  of  the 
good  conducting  quality  of  these  metals,  weight  considered,  the 


48       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

indications  of  the  instrument  become  "  dead-beat,"  that  is,  when 
current  is  applied,  the  coil  swings  at  once  to  the  position  corre- 
sponding to  the  current  strength  without  oscillation  around  it. 
When  the  coil  swings,  the  metallic  frame  acts  like  a  short-cir- 
cuited- conductor  in  a  motor  armature  ;  the  currents  circulating 
therein  require  energy  for  their  generation,  and  that  energy  is 
deducted  from  the  momentum  of  the  moving  parts,  causing  them 
to  come  to  rest  almost  instantly. 

In  the  original  form  of  D'Arsonval  galvanometer  just  de- 
scribed, the  field  is  not  uniform,  as  the  air  gap  between  the 
cylindrical  core  and  the  plane  faces  of  the  magnet  is,  of  course,  of 
different  depth  at  different  points.  As  the  torsional  reaction  of 
the  suspension  fibers  increases  in  direct  proportion  to  the  angle 
of  twist,  deflections  that  are  directly  proportional  to  the  current 
strength  are  obtained  only  when  the  coil  revolves  in  a  iinif orm 
magnetic  field.  A  uniform  field  may  be  obtained  by  shaping  the 
poles  of  the  magnet,  so  that  they  embrace  the  central  core  and 
leave  a  uniform  air  gap,  or  the  same  end  may  be  attained  by 
attaching  to  the  magnet  poles,  iron  extension  pieces  similarly 

shaped.  It  is  convenient  to  have  an 
instrument  in  which  the  angular  de- 
flections are  in  direct  proportion  to 
the  current  'strength,  as  this  greatly 
facilitates  the  comparison  of  different 
currents  with  one  another. 

It  is  claimed  by  some  authorities  that 
the  most  efficient  form  of  the  moving 
coil  is  a  shuttle  shape  without  a  cen- 
tral core,  instead  of  the  rectangular  one 
employing  a  core.  A  modern  galva- 
nometer in  which  this  construction  is 
employed  is  shown  in  Fig.  31.  It  will 
be  noted  that  here  the  magnet  is  placed 
horizontally,  instead  of  vertically,  and 
composed  of  a  large  number  of  com- 
paratively thin  separate  magnets  stacked 
one  on  top  of  another.  Instead  of 
shielding  the  whole  instrument  by  a  glass  bell  jar,  the  revolv- 
ing coil,  suspension,  and  mirror  are  enclosed  in  a  brass  tube,  a 
small  glass  window  being  provided  opposite  the  iniiror,  through 


FIG.  31. 


GALVANOMETERS.  49 

which  the  beam  of  light  indicating  the  extent  of  motion  may 
pass.  The  complete  brass  tube  with  its  contents  may  be  re- 
moved from  the  magnetic  structure  without  disturbing  any 
connection,  as  contacts  are  made  with  the  coil  through  sta- 
tionary spring  plates  in  electrical  contact  with  the  terminal 
binding  posts. 

Instruments  so  built  may  be  made  of  very  high  sensibility, 
for  instance,  one  having  a  resistance  of  about  200  ohms  may  be 
able  to  show  a  deflection  of  the  beam  of  light  thrown  from  a 
fixed  source  to  the  mirror  carried  by  the  moving  system,  and 
back  again  to  a  fixed  translucent  scale  placed  1  meter  away 
from  the  instrument,  of  1  millimeter  when  200  megohms  are 
placed  in  series  with  the  galvanometer,  and  a  potential  of  1  volt 
applied  to  the  free  galvanometer  and  resistance  terminals  re- 
spectively. With  a  coil  having  a  resistance  of  about  3,500 
ohms  1  millimeter  deflection  can  be  had  through  about  1,500 
megohms  with  1  volt. 

It  must  be  confessed  that  these  stated  sensibilities  are  some- 
what misleading,  as  they  are  due  in  part  to  using  a  suspension 
fiber  that  is  so  delicate  that  elastic  fatigue  will  often  become 
noticeable.  With  such  high  sensibility  instruments  it  is  by  no 
means  uncommon  to  have  the  light  spot  on  the  scale  refuse  to 
return  to  the  zero  mark  after  current  is  cut  off,  at  least  until 
the  lapse  of  a  period  that  may  be  reckoned  in  hours,  and  some- 
times even  days.  The  low  mechanical  strength  of  the  suspen- 
sions introduces  another  objectionable  feature,  their  great 
liability  to  rupture.  Means  are  usually  provided  for  removing 
the  strain  on  the  suspension  and  then  firmly  clamping  the  coil 
when  the  instrument  is  to  be  transported,  but  the  suspensions 
are  nevertheless  frequently  broken  after  the  galvanometers  are 
set  up,  and  their  replacement  is  then  tedious  work.  Not  only 
is  time  required  for  the  delicate  operation  of  replacing  the 
broken  suspension,  but  the  calibration,  namely,  the  deflection, 
given  by  a  stated  current  must  be  determined  afresh.  This  is 
different  for  different  suspensions,  not  so  much  because  these 
vary  in  resistance,  for  their  resistance  is  generally  negligible  as 
compared  with  that  of  the  coil  and  the  external  circuit,  but 
because  of  the  different  torsional  rigidity  of  different  speci- 
mens. As  the  latter  are  commonly  made  by  flattening  a  wire 
of  a  diameter  of  about  .002  inches  in  a  set  of  jeweler's  rolls,  it 


50        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

is  practically  impossible  to  get  the  resulting  .strips  of  uniform 
size  and  uniform  elasticity. 

One  other  objection  to  this  sensitive  form  of  D' Arson val  gal- 
vanometer is  the  fact  that  the  mechanical  clearance  between 
the  coil  and  the  magnet  face  is  reduced  to  a  minimum  in  order 
to  reduce  the  length  of  the  air  gap  in  the  magnetic  circuit  and 
therefore  increase  the  density  of  the  lines  of  force  flowing  there- 
through. Because  of  this  small  clearance  it  becomes  necessary 
to  level  the  instrument  with  exceeding  care  so  that  the  coil 
may  not  touch  the  poles  at  any  point.  On  the  other  hand,  they 
are  valuable  in  workshops  and  laboratories,  because  they  com- 
bine with  high  sensibility  immunity  from  disturbance  by  stray 
magnetic  fields,  as  the  one  in  which  the  coil  swings  is  so  very 
strong  as  to  mask  any  others  that  are  apt  to  exist  at  the  point 
of  use. 

A  form  of  D'Arsonval  galvanometer  that  is  almost  entirely 
free  from  the  objections  to  which  the  sensitive  form  is  open,  but 
which,  on  the  other  hand,  is  of  lesser  sensibility,  is  illustrated 
in  Fig.  32.  This  Chauvin  and  Arnoux  instrument  is  like  the 
original  D'Arsonval  pattern,  in  that  a  central  stationary  core  is 
used.  The  coil  consists  of  a  rectangular  copper  frame  around 
which  is  wound  the  moving  wire.  It  does  not  require  the  spe- 
cial leveling  screws  employed  in  the  high  sensitive  form,  as  it  is 
provided  with  a  gimbal  interposed  between  the  instrument 
proper  and  the  wall-plate,  which  device  of  course  makes  the 
instrument  hang  perfectly  vertical  if  the  plate  is  screwed  upon 
the  wall.  The  suspension  for  the  coil  also  differs  from  those 
in  the  high  sensibility  devices ;  it  is  formed,  not  of  a  straight 
thin  strip  of  bronze,  but  a  strip  of  very  elastic  high  conductivity 
alloy  wound  helically  about  a  mandrel  that  is  about  as  big  as 
a  knitting  needle.  The  toughness  of  these  suspensions  is 
almost  incredible,  being  such  that  the  makers  find  it  entirely 
superfluous  to  supply  any  means  of  blocking  the  coil  while  in 
transit.  They  can  be  shipped  around  by  express,  and  the 
writer  has  even  known  of  one  being  thrown  to  the  ground  with 
such  violence  that  the  mirror  became  dislodged  without  caus- 
ing the  suspension  to  break  or  to  be  deformed  sufficiently  to 
prevent  the  coil  from  swinging  freely  in  its  allotted  position 
when  the  instrument  was  again  hung  up.  This  same  suspen- 
sion is  of  advantage  where  mechanical  vibration  exists  at  the 


GALVANOMETERS. 


51 


point  of  installation,  as  it  serves  to  cushion  that  vibration  and 
greatly  diminishes  the  dancing  about  of  the  light  spot  that  is 
so  objectionable  in  the  high  sensibility  form  and  frequently 
renders  it  impossible  to  take  any  readings  whatsoever.  In.  the 
Chauvin.  and  Arnoux  instrument  the  support  for  the  scale  is 
arranged  to  be  carried  by  the  instrument  itself,  and  the  tele- 
scope method  (see  page  43)  of  making  readings  is  employed  in 
order  to  render  unnecessary  the  employment  of  a  source  of 
artificial  light.  It  is  very  light  and  so  small  that  when 


FIG.  32. 

the  scale  support  and  scale  is  removed  it  may  be  carried  in 
a  coat  pocket.  With  1  meter  distance  between  the  mirror 
and  the  scale  an  instrument  having  a  resistance  of  about  175 
ohms  will  give  a  deflection  of  somewhat  over  1  millimeter  with 
1  volt  when  about  90  megohms  are  inserted  in  series.  Com- 
paring this  with  the  high  sensibility  form,  it  will  be  seen  that 
the  sensibility  of  the  Chauvin  and  Arnoux  pattern  is  less  than 
one  half  as  great. 

In  the  D'Arsonval   instruments  mentioned   above,  the  force 


52        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


Flexible 


FIG.  33. 


that  opposes  the  motion  of  the  coil  is  that  offered  by  a  strip  of 
elastic  metal  which  is  being  put  under  torsion.  An  interesting 
variation  is  where  the  elasticity  of  the  suspension  is  made  as 

small  as  possible  and  the 
opposing  force  supplied  by 
magnetic  attraction.  Refer- 
ring to  Fig.  33,  if  the  fila- 
ments attached  to  the  mov- 
ing coil  are  conductors,  but 
so  flexible  that  they  offer 
practically  no  resistance  to 
the  rotation  of  the  coil,  any 
current  that  may  be  passed 
would  cause  the  coil  to 
move  and  assume  apposition 
where  its  plane  is  at  right 
angles  to  the  direction  of 
the  lines  of  force  in  the  field 
between  the  two  magnetic 
poles.  If,  however,  the  wire 
forming  the  coil  is,  as  was  suggested  many  years  ago  (British 
patent,  No.  8,795,  of  1887,  to  Ayrton  and  Perry),  of  iron,  or  is 
wound  on  rectangular  iron  form,  the  mag- 
netic flux  between  the  poles  will  tend  to 
hold  the  coil  so  that  its  plane  is  parallel 
to  the  direction  of  the  lines  of  force,  and 
the  further  the  plane  of  the  coil  departs 
from  this  position  by  rotating  around  the 
axis  formed  by  suspension  fiber,  the 
greater  is  the  force  tending  to  bring  it 
back  again.  We  therefore  have  the 
opposing  force  furnished  by  a  body  that 
is  influenced  by  the  same  magnetic  force 
whose  reaction  with  the  current  causes 
the  coil  to  move.  This  tends  to  pre- 
serve stability  of  calibration,  for  if  the 
strength  of  the  fixed  magnet  decreases, 
the  reaction  between  it  and  a  given  cur- 
rent in  the  coil  decreases,  but  the  force  opposing  the  coil 
motion  likewise  diminishes  as  the  effort  to  hold  the  iron  ele- 


Fio.  34. 


GALVANOMETERS.  53 

ment  in  line  is  no  longer  as  great.  This  form  of  galvanometer 
has  been  reinvented  of  late  by  Mr.  Weiss,  and  was  described  by 
him  in  a  communication  to  the  French  Academy  of  Science  in 
the  early  part  of  1902.  Fig.  34  shows  the  instrument.  The 
iron  element  here  takes  the  form  of  a  short  bar,  M.  It  is. 
claimed  that  the  strength  of  the  magnet  may  vary  as  much 
as  20  per  cent  without  changing  the  calibration.  Pivot-borne 
instruments  of  this  class,  for  commercial  measurements  of  cur- 
rent and  voltage,  have  likewise  recently  been  placed  on  the 
market  in  this  country. 

REFLECTING   ELECTRO-DYNAMOMETERS. 

The  preceding  instruments  are  suitable  only  for  the  measure- 
ment of  direct  currents,  because  the  field  furnished  by  the  per- 
manent magnet  is  constant  in  direction,  so  that  if  the  current 
passed  through  the  movable  coil  be  reversed,  the  deflecting  force 
is  reversed  also.  The  inertia  of  the  coil  will  not  allow  it  to 
follow  these  reversals,  so  the  only  effect,  if  an  alternating  current 
is  applied,  will  be  a  slight  trembling  of  the  mirror  and  the  beam  of 
light  reflected  therefrom.  A  moving  coil  galvanometer,  which 
responds  to  either  direct  or  alternating  current,  is  called  an 
electro-dynamometer,  an  example  of  which,  well  known  in  this 
country,  is  the  form  designed  by  the  late  Professor  Rowland. 
In  it  the  field  in  which  the  moving  coil  swings  is  supplied  by  a 
stationary  coil  of  wire.  Through  this  coil  is  passed  current  de- 
rived from  the  same  source  as  that  flowing  through  the  movable 
coil.  In  this  apparatus,  even  if  the  current  be  constantly  chang- 
ing in  direction,  that  in  the  fixed  and  movable  coils  is  simul- 
taneously reversed,  the  resultant,  therefore,  being  a  constant 
effort  to  turn  the  coil  in  one  direction.  As  is  shown  in  the  dia- 
grammatic illustration  in  Fig.  35,  there  are  two  fixed  coils,  one  of 
fine  wire  of  many  turns,  and  the  other  of  coarse  wire  of  few 
turns,  these  being  introduced  in  order  to  extend  the  range  of  the 
instrument  and  make  its  capacity  suited  to  the  measurement  of 
both  large  and  small  currents.  Separate  terminals  are  provided 
for  each  winding  so  that  they  may  be  interconnected  in  any 
way  desired.  It  is  not  feasible  to  make  the  indications  of  this 
class  of  galvanometers  "  dead  beat "  by  winding  the  movable 
coil  on  a  metallic  frame,  for  if  this  were  done  currents  would 
be  induced  in  that  frame  when  alternating  currents  passed 


54        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

through  the  fixed  coil,  and  the  repulsion  between  these  currents 
would  cause  a  deflection,  even  if  no  external  current  at  all  were 
applied  to  the  moving  one.  The  oscillations  are  therefore 
damped  by  mechanical  means,  a  vane  of  mica  being  secured  to 
the  moving  coil  and  fitted  closely  in  a  stationary  air-tight  box. 
The  sensibility  of  these  instruments  is  by  no  means  as  great  as 
galvanometers  of  the  D'Arsonval  type,  as  the  magnetic  field 
furnished  by  the  fixed  coils  is  of  far  less  intensity.  It  is, 

however,  sufficiently 
great  so  that  an  alter- 
nating current  of  .0001 
ampere,  or  an  alter- 
nating potential  of 
.005  volt  may  be  meas- 
ured. The  sensibility 
for  direct  current  is 
somewhat  higher,  but 
many  precautions  must 
be  observed  in  direct 
current  measurements 
with  reflecting  electro- 
dynamometers,  in 
order  to  eliminate  the 
influence  of  foreign 
magnetic  fields,  nota- 
bly the  earth's  field 
as  modified  by  mag- 
netic bodies  in  the 
vicinity  of  the  appa- 
ratus. A  complete 
Rowland  electro-dyna- 
mometer is  illustrated  in  Fig.  36.  It  will  be  noted  that  deflec- 
tions of  the  moving  part  are  observed  with  the  aid  of  a  tele- 
scope and  fixed  scale,  as  described  on  page  44. 

MOVING   MAGNET    GALVANOMETERS. 

Galvanometers  in  which  the  magnet  moved  and  the  coil  con- 
veying the  current  to  be  measured  was  held  stationary,  formed 
the  earliest  type  of  these  instruments.  In  their  elementary 
form  such  galvanometers  consisted  of  a  compass  needle  sup- 


FIG.  35. 


GALVANOMETERS. 


55 


ported  on  a  pivot,  which  was  deflected  by  current  passed,  par- 
allel to  its  length,  over  and  under  several  times,  through  a  coil 
of  wire.  The  natural  evolution  of  this  form  led  to  an  instru- 
ment in  which  the  needle  was  suspended  by  a  fine  silken  fiber 
which  introduced  a  far  smaller  error  due  to  torsional  rigidity  in 
the  fiber  than  was  introduced  by  the  friction  between  the  pivot, 
and  the  jewel  resting  thereon.  Of  course,  the  deflection  caused 
by  a  given  current  is  increased  in  proportion  to  the  number  of 
times  that  the  current  acts  on  the  needle,  in  other  words,  by 
having  an  increased  number  of  turns  in  the  coil  surrounding  it 


TIG.  36. 

This  expedient  cannot  be  carried  too  far,  however,  as  increased 
turns  mean  an  increased  length  of  wire,  and  hence  resistance  for 
the  current  to  overcome,  and  the  last  turns  are  necessarily 
further  removed  from  the  needle  than  the  earlier  ones,  and 
hence  of  less  efficiency.  The  next  step  to  increase  sensibility 
is  to  decrease  the  directive  force  tending  to  hold  the  needle  in  a 
given  position.  If,  as  is  usually  the  case,  the  directive  force  is 
that  due  to  the  earth's  field,  its  intensity  may  be  diminished  by 
placing  a  permanent  magnet  near  the  apparatus,  in  such  a  posi- 
tion that  the  field  surrounding  it  is  opposite  to  the  earth's  field. 
The  magnet  is,  of  course,  not  adjusted,  so  that  its  field  and  the 


56       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

earth's  field  entirely  neutralize  one  another,  as  this  means  no 
directive  force  whatsoever.  It  can,  however,  be  adjusted  so 
that  one  or  the  other  preponderates  but  slightly,  and  the  sensi- 
bility of  the  apparatus  is  correspondingly  increased.  At  this 
point  it  might  be  noted  that  it  is  possible  to  make  the  movable 
element  of  a  moving  magnet  galvanometer  of  a  weight  the  frac- 
tion of  that  of  the  coil  in  the  D'Arsonval  type,  and  hence  far 
finer  suspensions  are  permissible,  with  a  resulting  decrease  of 
the  force  necessary  to  twist  them  through  a  given  angle  and  a 
corresponding  increase  of  sensibility.  As  it  is  not  necessary 
to  convey  currents  to  and  from  the  movable  element  through  the 


FIG.  37. 

suspensions,  only  one  need  be  used,  and  that  may  be  of  noncon- 
ducting material.  These  features  contribute  to  high  sensibility. 
A  prominent  moving  magnet  galvanometer  of  the  above  de- 
scribed type  is  the  "  Kelvin  instrument,"  illustrated  in  Fig.  37. 
The  magnet  here  takes  the  form  shown  in  Fig.  38,  where  three 
short  pieces  of  watch  spring  are  flattened  out  and  cemented  to  a 
mica  disk  supported  by  a  quartz  or  silk  fiber.  This  construc- 
tion is  very  light  and  compact.  In  the  Kelvin  instrument,  the 
current-carrying  coil  is  divided  up  into  two  halves,  one  of  which 
is  movable,  so  that  access  may  be  had  to  the  magnet  system, 


GALVANOMETERS. 


57 


FIG.  38. 


and  the  suspension  renewed,  if  broken.  The  magnet  for  varying 
the  sensibility,  by  neutralizing,  the  earth's  held  to  a  greater  or 
less  degree,  is  not  shown  in  Fig.  37.  It  is  arranged  below  the 
apparatus  and  equipped  with  a  slow-motion  screw,  so  that  a  fine 
adjustment  of  the  position  of  the  directive 
magnet  relative  to  the  moving  needle  is  pos- 
sible. 

This  particular  class  of  Kelvin  instrument 
is  objectionable  because  of  its  extreme  sensi- 
bility to  disturbances  due  to  stray  magnetic 
fields.  If  the  control  magnet  is  adjusted 
almost  to  neutralize  the  controlling  effect  of 
the  earth's  field,  any  minute  variation  of  the 
latter  due  to  the  presence  of  magnetic  bodies 
will  cause  the  needle  to  deflect ;  the  same  effect 
being,  of  course,  caused  by  neighboring  current- 
carrying  conductors  which  set  up  fields  modi- 
fying the  influence  of  the  earth's  field.  This 
sensibility  to  magnetic  disturbances  may  be 
partially  overcome  as  follows  :  Referring  to  Fig.  39,  if  two  mag- 
netized needles  of  like  strength  are  rigidly  coupled  together  with 
their  ends  of  the  same  magnetic  polarity  pointing  in  opposite 
directions,  the  tendency  of  the  earth's  field  to  keep  one  needle 
in  a  given  position  is  evidently  opposite  to  and  neutralized  by 
its  tendency  to  keep  the  other  needle  in  just  the  reverse  posi- 
tion. Such  a  magnetized  pair  will  therefore  take  up  any 
position  freely  when  in  a  field  as  nearly  uniform  as  that  of  the 
earth,  and  is  said  to  be  "  astatic."  An 
astatic  couple  for  a  Kelvin  instrument  is 
formed  by  rigidly  joining  together  in  a  simi- 
lar way  two  of  the  sets  of  magnetized  watch 
springs  cemented  to  mica  disks  used  in  the 
plain  instrument  just  described.  Both  the 
upper  and  lower  elements  are  surrounded 
by  wire  coils  interconnected  so  that  the  sum 
of  all  the  efforts  is  to  cause  the  element  to 
rotate  in  a  given  direction.  Each  of  the  two  coils  is  wound 
in  two  sections,  as  in  the  case  of  the  simpler  instruments,  and 
one  pair  of  these  is  likewise  movable,  in  order  that  access  may 
be  had  to  the  moving  part.  Fig.  40  shows  a  four-coil  Kelvin 


S 


FIG. 


58       ELECTRIC  AND   MAGNETIC  MEASURENENTS. 

galvanometer,  the  second  illustration  showing  the  front  coils 
swung  down  out  of  the  way  and  the  tube  carrying  the  magnets 
swung  out  from  the  rear  coils  in  order  that  free  access  may  be 
had  all  around  it.  The  mirror,  as  will  be  noted,  is  fastened  to 
the  rod  joining  the  two  magnetic  elements,  midway  between 
them.  The  other  cut  in  Fig.  40  shows  the  instrument  assem- 
bled and  the  directive  magnet  below  it.  This  magnet  is  closer 
to  the  lower  set  of  needles  than  the  upper  one,  and  hence,  in- 
fluences the  latter  more  and  furnishes  a  directive  force  sufficient 
to  hold  it  in  a  given  position.  The  four  coils  may,  of  course, 
be  coupled  together  in  series  or  parallel  as  desired,  or  in 


FIG  40. 

opposition,  namely,  differentially,  so  that  the  deflection  due  to 
the  difference  between  the  strength  of  two  currents  may  be 
observed. 

The  construction  of  these  instruments  is  not  such  that  the  in- 
dications are  inherently  "  dead  beat,"  and  it  is  necessary  to  apply 
extraneous  methods  of  damping  if  rapid  readings  are  to  be  taken. 
In  some  forms  this  is  accomplished  by  attaching  to  the  moving 
system  a  thin  vane  immersed  in  oil,  but  it  is  more  common  to 
make  the  mica  disks  on  which  the  magnetized  watch  springs  are 
cemented  fit  rather  closely  in  a  spherical  chamber  so  that  the 


GALVANOMETERS.  59 

indications  are  air  dampened.  If  the  hollow  chamber  has  mas- 
sive copper  walls,  this  also  damps  the  oscillations,  as  the  moving 
magnet  expends  energy  in  setting  up  currents  in  the  copper  and 
there  is,  hence,  less  force  available  to  move  it  beyond  the  posi- 
tion corresponding  to  the  current  strength. 

The  four-coil  Kelvin  galvanometer,  notwithstanding  the  fact 
that  it  is  provided  with  an  astatic  pair  of  needles,  is  by  no  means 
entirely  immune  from  disturbances  by  external  magnetic  forces. 
This  is  because  it  is  seldom  that  such  forces  are  sensibly  the 
same  in  the  regions  of  both  magnets ;  or,  in  other  words,  that 
such  external  fields  of  force  are  uniform. 

It  is  also  exceedingly  susceptible  to  mechanical  vibrations  and 
must  be  mounted  with  extreme  care  in  order  that  such  vibrations 
may  not  affect  it  sufficiently  to  throw  the  light  spot  off  the 
scale.  On  the  other  hand  these  galvanometers  have  the  highest 
sensibility  attainable. 

HOT    WIRE    GALVANOMETERS. 

When  an  electric  current  flows  through  a  conductor,  a  resist- 
ance to  that  flow  is  encountered,  and  the  work  done  by  the  cur- 
rent in  overcoming  the  resistance  heats  the  conductor.  If  the 
conductor  is  a  fine  wire  and  the  current  is  comparatively  heavy, 
the  resultant  expansion,  suitably  multiplied  and  indicated,  may 
be  used  to  measure  the  current  -strength.  The  use  of  gal- 
vanometers utilizing  this  principle  is  not  general,  because  their 
sensibility  is  not  high ;  they  are  sluggish  in  their  indications, 
owing  to  the  time  required  for  the  wire  to  attain  its  new 
temperature  when  the  current  strength  changes,  and  it  is 
difficult  to  compensate  for  changes  in  the  temperature  of  the  air 
surrounding  them  and  to  shield  the  wire  from  slight  air  currents. 

On  the  other  hand,  they  have  the  great  advantage  for  alter- 
nating current  measurements,  that  their  self-induction  and 
capacity  is  practically  zero,  and  hence  their  use  does  not  alter 
circuit  conditions. 

One  of  the  most  sensitive  instruments  of  this  class  consists 
of  two  very  fine  wires  of  manganin  or  platinum  silver  alloy 
stretched  parallel  to  one  another  a  short  distance  apart,  their 
ends  being  secured  to  appropriate  abutments.  These  wires  are 
embraced  at  the  center  by  a  very  small  loop  of  stiff  paper  carry- 
ing a  small  plane  mirror.  A  microscopic  hook  at  the  end  of  a 


60       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

fine  light  spring  is  slipped  over  one  of  the  wires  near  the  paper 
loop,  the  mirror  in  this  way  being  pulled  around  to  a  certain 
angle  about  the  other  wire  as  a  center.  When  current  flows 
through  the  wire  on  which  this  hook  is  caught,  the  expansion 
of  the  wire  due  to  its  heating  allows  the  spring  to  pull  the 
mirror  over  still  further,  the  resultant  deflection  being  read  off 
on  a  suitable  scale  by  the  conventional  spot  of  light.  For  max- 
imum sensibility  to  small  currents,  the  wires  are  made  of  a 
material  having  as  high  a  specific  resistance  as  can  be  obtained 
in  order  to  make  the  heating  effect,  which,  with  a  given  current, 
varies  as  the  resistance,  a  maximum.  To  get  the  greatest 
deflection  with  a  low  voltage  the  wires  are  made 
of  as  low  resistance  as  is  feasible,  in  order  that  a 
maximum  current  strength  may  flow  and  hence 
cause  maximum  elongation. 

Several  galvanometers  working  on  this  principle 
have  been  brought  but  from  time  to  time,  notably 
those  of  Prof.  Threlfall  and  of  Dr.  Fleming.     In 
this  country,  a  similar  instrument  is  made  by  Leeds 
,nd  Northrup. 

RADIATION    GALVANOMETERS. 

The  most  sensitive  galvanometers  for  the  detec 
tion  of  alternating  currents  seem  to  be  those  in 
which  the  heating  of  a  wire  carrying  current  is 
indicated,  not  by  a  magnification  of  the  change 
in  length  of  the  wire,  but  by  radiation  of  its  heat 
to  a  delicate  thermo-couple.  The  Duddell  instru- 
ment, made  on  this  principle,  is  diagrammatically 
illustrated  in  Fig.  40  A.  As  will  be  seen  from 
this,  a  loop  consisting  of  a  single  turn  of  wire  is  placed  in  the 
field  of  a  magnet  like  that  in  the  conventional  D'Arsonval 
galvanometer.  The  two  ends  of  the  loop  terminate  in  a 
thermo-couple,  which  is  placed  close  to  the  short  straight  wire 
through  which  the  current  to  be  measured  is  led.  The  heat 
radiated  from  the  wire  causes  a  current  to  flow  from  the 
thermo-couple  through  the  loop,  and  that  current  brings  about 
a  deflection  of  the  loop  in  the  conventional  manner.  The  deflec- 
tions are  read  off  by  the  aid  of  the  mirror,  M,  in  the  ordinary 
way.  According  to  Duddell,  such  a  galvanometer  will  show  an 


FIG.  40  A. 


GALVANOMETERS.  61 

apparent  scale  deflection  of  2  millimeters  with  1  millivolt 
difference  of  potential,  at  the  resistance  wire  ends.  The  cur- 
rents generated  by  talking  into  a  Bell  telephone  receiver  are 
sufficient  to  throw  the  beam  of  light  entirely  off  the  scale.  An 
instrument  having  a  resistance  of  18  ohms  is  capable  of  meas- 
uring a  current  as  low  as  160  micro-amperes. 

REFLECTING    ELECTROMETERS. 

The  electrostatic  instrument  shown  in  its  elementary  form  in 
Fig.  19  and  described  on  page  30,  may,  when  suitably  designed 
and  provided  with  a  long,  delicate  suspension  and  a  mirror  for 
taking  readings,  be  made  a  galvanometer  of  value  for  certain 
alternating  and  direct  current  measurements.  Its  sensibility  is 
by  no  means  as  high  as  that  of  a  very  ordinary  direct  current  gal- 
vanometer or  of  the  galvanometer  responsive  to  both  direct  and 
alternating  currents  just  described,  but  it  has  the  advantage  of 
possessing  a  practically  infinite  resistance,  no  inductance  and 
small  capacity.  The  first  of  these  characteristics  is  of  peculiar 
advantage  in  certain  direct  as  well  as  alternating  current  meas- 
ments  as  the  electromotive  force  measured  by  the  twisting  of  the 
suspension  as  shown  by  the  deflection  of  the  beam  of  light 
from  its  mirror  is  that  of  the  source  under  test  when  it  is 
supplying  no  current,  that  is  to  say,  it  is  the  open  circuit 
E.M.F.,  a  value  that  often  requires  determintion. 

In  using  electrostatic  galvanometers,  there  is  a  source  of 
possible  error  which  must  always  be  considered.  The  suspension 
fiber  supporting  the  movable  vane  in  such  instruments  must 
necessarily  be  a  conductor  of  electricity  in  order  that  the  cur- 
rent required  to  charge  the  vane  may  be  conveyed  to  it.  The 
fiber  and  the  vane  are  almost  invariably  of  different  chemical 
composition,  usually  phosphor  bronze  and  aluminum  respectively, 
and  when  two  dissimilar  metals  are  placed  in  contact  it  is  well 
known  that  there  will  exist  a  difference  of  potential,  usually 
called  a  "  Contact  E.M.F."  between  them.  The  movable  ele- 
ment thus  always  has  a  small  initial  charge,  and  if  it  is  further 
charged  by  applying  current  to  the  apparatus  in  such  a  direction 
that  the  new  charge  assists  the  initial  one,  the  deflection  will 
be  greater,  by  twice  that  due  to  the  initial  charge,  than  if  the 
potential  of  the  circuit  to  be  measured  were  applied  in  the 


62        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

opposite  direction.  If  the  instrument  is  always  to  be  used 
with  direct  current,  and  care  is  taken  to  see  that  the  same  pole 
of  the  applied  circuit  is  always  attached  to  a  given  binding 
post,  this  error  may  be  allowed  for  in  the  calibration.  If  alter- 
nating current  be  measured,  however,  a  correction  equal  to  the 
initial  charge  must  be  applied.  A  reflecting  electrometer  is 
shown  in  Fig.  41. 

For  the  very  highest  sensibilities  the  suspension  for  the 
moving  element  of  an  electrometer  may  be  made  of  a  quartz 
fiber  on  which  is  chemically  precipitated  a  very  thin,  adherent 

film  of  gold  to  render  it  con- 
ducting. With  a  suspension 
of  this  sort  a  sensibility  may 
be  obtained  such  that  it  is 
possible  to  get  a  deflection  of 
200  or  more  millimeters  on 
a  scale  placed  1  meter  away 
from  the  mirror  with  1  volt. 
As  the  deflections  of  electro- 
static instruments  increase  as 
the  square  of  the  applied  vol- 
tage, a  very  high  deflection 
for  a  given  E.M.F.  may  evi- 
dently be  obtained  by  apply- 
ing a  steady  initial  E.M.F.  of 
some  magnitude  and  then 
superimposing  the  unknown 
one  on  that.  In  this  way  the  sensibility  of  a  reflecting  electro- 
meter may  be  increased  enormously. 

THE    TELEPHONE   RECEIVER. 

The  conventional  telephone  receiver  is  a  convenient  and 
simple  piece  of  apparatus  often  used  for  the  detection  of  feeble 
electric  currents. 

Of  course,  it  cannot  of  itself  measure  current  strength  as  its 
indications  are  audible  only,  and  the  human  ear  cannot  evaluate 
tone  volume  with  any  accuracy,  but  it  does  form  a  sensitive 
means  for  showing  whether  a  difference  of  potential  does  or 
does  not  exist.  It  is  naturally  necessary  to  arrange  the  appara- 
tus so  that  the  circuit  through  the  receiver  may  be  successively 


FIG.  41. 


GALVANOMETERS. 


63 


made  and  broken,  because  it  is  only  on  the  make  and  on  the 
break  that  the  diaphragm  of  the  receiver  will  respond  and  give 
forth  a  clicking  sound. 

A  good  telephone  receiver  having  a  resistance  of  about  100 
ohms  will  give  an  audible  click  when  a  circuit  passing  .005  mil- 
liamperes  through  it  is  made  or  broken. 

The  advantages  of  a  telephone  receiver  for  this  kind  of  work 
are  its  low  cost,  its  portability,  the  fact  that  it  need  not  be 
leveled  or  placed  in  any  definite  position,  and  that  it  is  not 
affected  by  stray  magnetic  fields. 

CAPILLARY    ELECTROMETERS. 

An  effective  device  for  detecting  and  measuring  very  small 
direct  current  E.M.F.'s  is  made  by  enclosing  in  a  glass  tube  of 


FIG.  42. 


very  fine  Dore,  clean,  pure  mercury  and  a  strong  solution  of 
sulphuric  acid,  the  two  being  in  contact  with  one  another. 
When  a  potential  difference  is  applied  between  the  two  ends  of 
the  tube,  an  action  takes  place  at  the  surface  of  contact  between 
the  mercury  and  the  acid  which  causes  a  change  in  the  capillary 
pressure.  This  in  turn  causes  a  displacement  of  the  surface  of 
the  mercury  which,  while  small,  may  easily  be  read  with  the  aid 
of  a  microscope.  For  small  differences  of  potential  the  dis- 
placement is  directly  proportionate  to  the  potential. 

Obviously,  a  device  built  on  the  above  principle  may  assume 
many  forms.  In  Fig.  42  is  shown  the  Boley  type,  in  which  the 
mercury  is  contained  in  a  spherical  glass  chamber  A  which 


64         ELECTRIC   AND  MAGNETIC  MEASUREMENTS. 

communicates  with  the  acid  solution  at  e  through  the  fine  bore 
tube  t.  A  relatively  large  volume  of  the  electrolyte  L  is  pro- 
vided in  order  to  have  a  large  contact  area  available  between  it 
and  the  other  mercury  electrode  E  through  which  current  is 
introduced,  this  large  area  being  desirable  to  prevent  rapid 
polarization.  The  level  at  which  the  mercury  in  the  fine  bore 
tube  t  comes  in  contact  "with  the  electrolyte  can  obviously  be 
adjusted  by  varying  the  air  pressure  on  the  surface  of  the  mer- 
cury in  A  or  by  varying  the  depth  of  the  'electrolyte  in  its 
chambers. 

The  change  in  level  caused  by  the  application  of  an  E.M.F. 
to  the  instrument  is  observed  through  a  microscope,  an  apparent 
change  of  1  millimeter  being  shown,  with  a  magnifying  power 
of  100,  with  a  potential  change  of  .0024  volts.  The  instrument 
can  be  read  to  .0002  volts  without  difficulty  and  it  is  claimed 
that  the  changes  in  level  are  exactly  proportionate  to  Ihe  volt- 
age up  to  .01  volts. 

Capillary  electrometers  are  not  in  common  use  as  they  have 
unstable  zeros,  are  not  portable,  and  the  microscope  method  of 
taking  readings  is  very  hard  on  the  eyes. 

GALVAXOMETEK    SHUNTS. 

Plain  Shunts. 

A  commercial  galvanometer  is  naturally  made  of  the  highest 
sensibility  consistent  with  its  cost  and  type  in  order  that  it 
may  be  suitable  for  delicate  and  accurate  work. 

For  preliminary  measurements,  the  sensibility  of  an  average 
galvanometer  is  often  too  high,  however,  and  in  making  the 
first  adjustments,  currents  may  flow  that  will  either  burn  out 
the  windings  or  injure  the  device  mechanically  by  deflecting 
the  moving  portion  too  violently  against  the  stops  provided  to 
limit  the  motion.  An  arrangement  of  several  galvanometers  of 
varying  sensibility  to  be  used  successively  would  evidently  be 
both  awkward  and  costly.  Devices  are  therefore  supplied,  by 
the  aid  of  which  the  sensibility  of  a  given  galvanometer  may 
be  varied  from  its  maximum  by  successive  steps  to  any  desired 
minimum,  and  these  devices  are  called  "  galvanometer  shunts." 

Referring  to  Fig.43,  let  G  represent  a  galvanometer  of  resistance 
6r,  B  the  source  of  the  current  to  be  measured,  and  x  a  resist- 


GALVANOMETERS. 


.     65 


ance  which  may  be  inserted  between  the  galvanometer  terminals. 
From.  the  law  of  divided  circuits  (see  page  93),  the  resistance  of 
the  circuit  formed  by  the  galvanometer  and  the  shunt  x  con- 

nected to  its  terminals  is  -^-  —  and,  if  the  current  flowing  through 

the  battery  circuit  is  A  amperes,  the  fraction  thereof  that  flows 

Ax 
through  the  galvanometer  is  -^  —  —  .     To  take  a  concrete  case,  if 

G-  is  900  ohms,  and  x  is  made  100  ohms,  --.  —  zr-c  =  .1  of  the 


g  - 
0 


G 


battery  current  goes  through  the  galvanometer  and  the  same 
current  from  the  battery  that  would  cause  a  given  deflection 
with  no  galvanometer  shunt  will  cause  but  one  tenth  of  that 
deflection  with  the  shunt  attached, 
provided,  of  course,  that  the  gal- 
vanometer is  of  a  pattern  in  which 
the  deflections  are  proportionate 
to  the  current.  It  is  usual  to 
supply  a  set  of  shunt  resistances 
like  x  in  the  figure,  all  built  into 
one  case  and  having  suitable  bind- 
ing-posts for  the  attachment  of 
the  various  wires.  Such  shunts 
are  usually  made  1,  gL,  and  -Q±-$ 
of  the  galvanometer  resistance, 
reducing  the  sensibility  to  respectively  .1,  and  .01,  and  .001 
of  the  normal.  One  of  them  is  illustrated  in  Fig.  44.  In  order 
to  have  the  simple  decimal  relationship  between  the  value  of 
the  deflections  when  such  shunts  are  used,  it  is  evidently  neces- 
sary to  have  the  shunt  resistances  accurately  adjusted  to  work 
with  the  given  galvanometer.  A  separate  shunt-box  is  there- 
fore required  for  each  instrument. 


B 


FlG- 43- 


Compensated  Shunts. 

It  will  be  noticed  that  with  simple  shunts  of  the  character 
just  described,  the  combined  resistance  of  the  galvanometer  and 
shunt  will  vary  with  the  shunts  of  different  values.  This  is  a 
feature  that  is  often  objectionable,  because  with  a  given  source 
of  E.M.F.  the  current  through  the  galvanometer  circuit  will 


66        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


vary  with  every  step.  It  is  therefore  evident,  if  we  have 
a  given  E.M.F.  which  produced  a  given  deflection  with  the  one 
tenth  shunt  in,  this  deflection  is  not  one  tenth  of  that  which 
would  have  been  given  with  the  same  E.M.F.  and  no  shunt,  but 
differs  by  an  amount  dependent  on  the  resistance  of  both  shunt 
and  galvanometer.  To  correct  this,  compensated  shunt-boxes 
are  made,  in  which,  when  the  movable  plug  is  shifted  to  insert 
any  ratio  shunt,  there  is  inserted  at  the  same  time  an  auxiliary 
resistance  in  the  galvanometer  circuit,  which  offsets  the  changed 
resistance  of  the  whole,  and  keeps  the  effective  resistance  be- 
tween the  battery  terminals  con- 
stant. The  way  in  which  this  is 
done  can  be  seen  from  inspection 
of  Fig.  45.  Owing  to  the  greater 
amount  of  work  involved  in  ad- 
justment, these  compensated*shunts 
are  far  more  costly  than  the  type 
described  before,  and  c  o  n  s  e- 
quently  are  in  less  common  use. 

The  Ayrton  Shunt. 

As  above  stated,  galvanometer 
shunts  of  the  types  just  described 
are  open  to  the  objection  that  each 
must  be  separately  adjusted  to 
work  with  the  galvanometer  with 
which  it  is  to  be  used.  This  is  a 
disadvantage  not  only  in  that  it 
necessitates  the  purchase  of  as 
many  shunts  as  the  user  has  instruments,  but  because  if  a  gal- 
vanometer should  be  injured  and  require  rewinding,  its  shunt 
would  have  to  be  readjusted  too,  thus  adding  considerably 
to  the  expense.  Such  shunts  are  also  objectionable  in  that, 
while  correct  for  a  steady  current,  the  indications  of  the  gal- 
vanometer with  which  they  are  used  are  not  correct  when  meas- 
uring current  impulses  that  exist  only  momentarily,  as  in 
measuring  capacity.  The  proof  of  this  need  not  be  given 
here,  although  it  may  be  of  interest  to  note  that  the  tendency 
is  to  make  the  galvanometer  read  too  low.- 

The  universal  shunt  devised  by  Ayrton  and  Mather  escapes 


FIG.  44. 


GALVANOMETERS. 


67 


these  objections.  This  shunt  is  universal  in  that  it  need  not 
be  adjusted  to  any  particular  galvaonmeter  but  can  be  used 
interchangeably  with  all,  and  the  results  are  accurate  whether 
the  current  flow  is  continuous  or  only  momentary.  The 
principle  of  the  Ayrton  and  Mather  shunt  can  be  understood 
from  Fig.  46.  Here  Q-  is  a  galvanometer  of  resistance  6r,  TT'  the 
resistance  which  is  connected  to  the  galvanometer  terminals  and 
forms  the  shunt  proper,  B  a  source  of  current,  C  the  current 
(total)  flowing  through  the  battery  circuit,  c  the  current  flowing 

through  the  galvanometer  cir- 
cuit, and  R  the  resistance  of  the 
conductor,  TT.f  From  the  law 
of  divided  circuits  the  current 
that  flows  through  the  galvano- 
meter is  C  = 


—r 


=  -^  —  —  ^  •     When  the  contact 

of  the  source  of  current  is  made 
at  the  extremities,  TT'  of  the 
shunt,  the  current  fl  o  w  i  n  g 
through  the  galvanometer  is  evi- 

~D 

dently  c  =__  .     If,  there- 

fore, r  be  made  -^  of  R,  only 
-J-g-  of  the  battery  current  goes 
through  the  galvanometer,  and 
the  deflection  for  a  given  bat- 
tery current  is  reduced  to  y1^. 
If  r  be  made  01  of  R,  only  T-J-g. 
of  the  battery  current  goes 
through  the  galvanometer,  and 
the  sensibility  is  reduced  to  that  amount.  A  commercial  form 
of  Ayrton  and  Mather  shunt  is  illustrated  in  Fig.  47.  Here 
there  are  four  steps  giving  sensibilities  of  1,  -1  and  of 


FIG.  45. 


the  normal  with  two  additional  steps,  one  short  circuiting 
the  galvanometer  when  no  current  is  on,  and  the  other  opening 
the  galvanometer  circuit  itself.  By  means  of  the  small  hard 
rubber  handle  shown,  the  contact  carriage  maybe  quickly  moved 
along  the  line  of  contacts,  the  galvanometer  being  watched  at 


68        ELECTRIC  AND   MAGNETIC  MEASUREMENTS. 

the  same  time,  until  a  sensibility  is  reached  which  gives  a  good 
deflection. 

ERECTION    AND    CAKE    OF    GALVANOMETERS. 

Generally  speaking,  the  higher  the  electrical  sensibility  of  a 
galvanometer,  the  more  it  is  subject  to  the  influence  of  mechan- 
ical vibration,  and,  if  placed  on  an  ordinary  work-bench  or 
table,  it  is  out  of  the  question  to  use  one  in  a  workshop ;  for 
the  trembling  of  the  mirror  causes  the  spot  of  light  to  jump 
over  the  scale  in  such  a  manner  that  no  readings  can  be  taken. 
A  frequently  adopted  plan  to  overcome  this  annoyance  is  to 
build  a  heavy  brick  or  stone  column,  capped  with  a  slab  of  soap- 
stone  or  slate,  on  which  the  galvanometer  may  be  placed  and 
leveled  for  use.  In  order  to  prevent  the  communication  of  the 
vibrations  of  the  building  thereto,  this  masonry  pier  must  be 
carried  clear  down  into  the  ground,  and  must  be  £ept  free 
throughout  its  whole  length  from  contact  with  any  part  of  the 


FIG.  46. 


building.  This  expedient,  of  course,  is  expensive,  and  local 
conditions  are  sometimes  such  that  even  it  does  not  afford  a 
complete  remedy ;  moreover,  the  construction  of  such  a  pier 
for  use  in  the  upper  stories  of  a  building  is  out  of  the  question. 

In  most  circumstances,  as  good  or  better  results  can  be 
secured  at  a  less  expense,  by  mounting  the  galvanometer  on  a 
heavy  timber  or  stone  shelf  built  solidly  into  the  walls  of  the 
building,  provided  the  machinery  foundations  are  separate  from 
the  foundations  of  the  walls.  With  a  reasonably  well-built 
structure,  and  not  too  much  moving  machinery  on  the  floors, 
good  results  may  be  obtained  some  stories  from  the  ground. 

In  cases  where  this  plan  does  not  give  a  sufficiently  steady 
support,  the  galvanometer  may  be  mounted  on  a  platform  hung 


GALVANOMETERS.  69 

from  springs,  and  provided  with  suitable  weights.  The  proper 
adjustment  of  the  weight,  with  respect  to  the  strength  of  the 
suspending  springs,  is  the  principal  feature  in  making  a  success 
of  the  method.  The  springs  should  be  rather  long,  moderately 
strong,  and  should  then  be  loaded  down  so  as  to  stretch  them 
well.  Thus  adjusted,  the  natural  period  of  oscillation  of  the 
apparatus,  as  regards  vertical  displacements,  is  large,  so  vertical 
tremors  of  a  comparatively  high  frequency  are,  practically 
speaking,  completely  damped  out.  High  frequency  disturbances 
in  a  horizontal  plane  are  still  more  completely  gotten  rid  of. 


FIG.  47. 


Should  there  be  a  tendency  for  the  apparatus  to  oscillate  in  its 
natural  period,  pendulum-wise  or  vertically,  it  can  be  overcome 
only  by  the  use  of  dash-pots  or  their  equivalent.  These  may 
be  arranged  to  damp  either  a  vertical  or  horizontal  oscillation. 
Another  good  way  to  damp  horizontal  movements  of  long 
period  is  to  fasten  rubber  bags  below  the  platform,  in  such 
positions  that  they  may  be  brought  into  contact  with  the  under 
side  of  the  platform  by  inflating  them  with  air.  This  will  stop 
the  long  period  movements,  while  the  bags  are  not  sufficiently 
rigid  to  communicate  short  period  movements. 

Fig.  48  shows  a  double  platform.     On  the  upper   shelf   is 


70        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

placed  the  principal  weight,  while  the  galvanometer  is  placed 
on  the  lower  shelf.  The  weights  and  springs  should  be  so  ad- 
justed that  the  natural  periods  of  the  two  shelves  are  incom- 
mensurable, which  still  further  tends  to  damp  out  vibrations 
of  all  frequencies.  This  arrangement  is,  however,  necessary 
only  under  exceptionally  unfavorable  circumstances. 

The  scale  on  which  the  deflections  of  the  beam  of  light  from 

y//////////////////^^^^^ 


FIG.  48. 


the  galvanometer  mirror  read  off  is  placed  on  a  separate  support, 
as,  in  the  case  of  the  pier  or  shelf  arrangement,  a  support  large 
enough  to  contain  both  would  be  too  costly,  and,  in  the  case  of 
the  spring  suspension  form,  both  bulky  and  offering  a  chance  of 
trouble  if  the  scale  should  be  accidently  touched  by  the  observer, 
as  this  would  then  set  the  whole  apparatus  in  vibration.  A 


GALVANOMETERS. 


71 


small  vibration  on  the  part  of  the  scale  is  of  little  importance,  as 
it  is  not  magnified  in  the  same  way  that  the  light  beam  motion 
is,  and  the  scales  are,  therefore,  usually  mounted  on  a  simple 
standard  at  the  proper  distance  from  the  galvanometer,  or,  in 
special  cases,  may  be  supported  from  overhead. 

In  that  form  of  reading  device  in  which  a  telescope  is  em- 
ployed, the  only  requisite  is  that  the  general  illumination  on  the 
scale  be  sufficient  to  make  the  scale  markings,  as  reflected  in 
the  mirror,  and  viewed  through  the  telescope,  readily  visible. 
In  the  pattern  where  a  beam  of  light  is  thrown  on  the  galva- 
nometer mirror,  and  reflected  from  there  by  a  translucent  scale, 
the  apparatus  must,  of  course,  be  placed  in  a  room,  which,  while 
it  need  not  be  absolutely  dark,  must  have  but  a  low 
illumination  in  order  that  the  position  of  the  line  of 
light  on  the  ground  glass  may  be  readily  discerned. 
The  source  of  the  beam  of  light  may  be  an  oil  lamp 
or  a  gas  jet,  inclosed  by  a  metal  chimney,  having  a 
fine  slot  in  one  side  through  which  the  ray  emerges. 
This  is  condensed  by  a  lense  and  thrown  on  the 
mirror,  the  latter  being  concave  to  prevent  disper- 
sion, and  makes  a  sharp  line  on  the  scale.  In  order 
to  obtain  a  darkened  galvanometer  room,  hangings 
are  usually  used,  which  interfere  with  the  circula- 
tion of  the  air,  and  the  room  is  apt  to  become  stuffy, 
if  gas  or  oil  flame  is  employed.  It  is  therefore 
still  better  to  use  an  incandescent  lamp  as  the  light 
source  where  possible.  The  lamp  should  not  have 
a  filament  of  the  coiled  form,  but  one  of  the  old 
plain  U  shape,  and  the  shield  around  the  lamp 
arranged  so  that  the  light  from  the  straight  portion 
of  one  of  the  halves  of  the  U  is  what  is  allowed  to  fall  on  the 
mirror.  Some  foreign  makers  go  so  far  as  to  construct  a 
special  incandescent  lamp  for  this  work,  in  which  one  leg  of  the 
filament  is  made  absolutely  straight.  An  example  of  this  is 
illustrated  in  Fig.  49. 

Few  general  instructions  can  be  given  in  a  work  of  this  kind 
as  to  the  care  of  a  galvanometer,  because  the  constructional 
details  vary  in  instruments  of  different  makes,  and  where  com- 
plete instructions  are  not  supplied  with  the  apparatus  by  the 
builders,  the  application  of  common  sense  will  remedy  the  defect. 


FIG.  49. 


72        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

Those  not  accustomed  to  handling  such  work  will  have  their 
patience  sorely  tried,  when  a  suspension  breaks  and  must  be  re- 
placed, but  they  must  console  themselves  with  the  reflection 
that  even  experienced  users  break  many  a  new  suspension  when 
replacing  an  old  one. 


CHAPTER    IV. 

POTENTIOMETERS. 
SLIDE    WIRE    TYPES. 

THE  potentiometer  is  an  instrument  of  precision  for  electri- 
cal measurements  that  is  sufficiently  important  to  warrant 
devoting  an  entire  chapter  to  its  uses.  With  its  aid,  and  that 
of  certain  auxiliary  appliances,  measurements  of  potential  may 
be  made  in  terms  of  the  E.M.F.  of  a  standard  cell,  covering  a 
range  of  from  a  very  small  faction  of  a  volt  to  several  thousand 
volts,  and  of  currents  from  a  fraction  of  an  ampere  to  many 
thousand  amperes.  It  may  also  be  used  for  the  accurate  com- 
parison of  resistances,  and  therefore  indirectly  for  the  meas- 
urement of  temperatures  varying  from  below  freezing  to 
1,200°  C. 

The  principle  of  the  ordinary  potentiometer  may  be  under- 
stood by  reference  to  the  accompanying  Fig.  50.  Here  MN  is 
a  straight  wire  of  convenient  length  and  as  high  resistance  as 
possible  consistent  with  mechanical  durability.  To  its  ends  are 
attached  leads  from  a  battery,  B,  usually  a  storage  cell  giving  a 
potential  of  about  two  volts,  in  circuit  with  an  adjustable  resist- 
ance, R,  by  means  of  which  the  difference  in  potential  between 
the  points  M  and  N  may  be  adjusted  to  any  desired  value 
lower  than  the  cell  potential.  To  the  point  M  there  is  also 
connected  a  wire  running  to  one  pole  of  a  double-throw  switch, 
D.  By  means  of  a  suitable  device,  6y,  contact  may  be  made  at 
any  desired  point  along  the  wire,  MN.  The  connection  running 
from  the  contact,  (7,  passes  through  the  galvanometer,  6r,  to  the 
other  pole  of  the  double-throw  switch,  D.  When  D  is  thrown 
to  the  position  shown  in  the  figure,  it  connects  the  wire  terminal 
attached  to  one  end  of  the  wire,  MN,  with  one  pole  of  a  standard 
cell,  S,  and  the  adjustable  contact,  (7,  with  the  other  pole  of  that 
cell.  When  the  switch,  D,  is  thrown  to  its  other  position,  the  same 
points  are  connected  with  the  unknown  E.M.F.  to  be  measured. 
The  standard  cell  has  a  resistance,  r  (usually  about  10, 000  ohms), 

73 


74        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

connected  in  series  .therewith,  which  resistance  may  be  short  cir- 
cuited by  the  switch  shown,  and  the  galvanometer  is  provided 
with  a  shunt,  $,  which  may  be  cut  in  or  out  by  means  of  its  switch. 
When  a  potential  measurement  is  to  be  made,  the  switch,  D,  is 
thrown  so  as  to  couple  in  the  standard  cell,  the  resistance,  r, 
being  in  the  standard  cell  circuit,  and  the  shunt,  S,  across  the 
galvanometer  terminals.  If  the  wire,  MN,  has  an  adjacent 
scale  divided  into  2,000  equally  spaced  divisions,  and  the  E.M.F. 
of  the  standard  cell  at  the  temperature  at  which  it  is  being 
worked  is  1.434  volts,  the  contact,  (7,  is  placed  1,434  divisions 
away  from  J/,  and  the  rheostat,  72,  varied  until  the  galvanom- 


FiG.  50. 

eter  shows  no  deflection.  The  shunt,  $,  across  the  galvanometer 
terminals  is  then  cut  out  so  as  to  increase  the  sensibility,  and  if 
the  galvanometer  then  shows  a  small  deflection,  the  rheostat,  R,  is 
further  adjusted  until  that  deflection  disappears.  As  -the 
strength  of  the  current  from  the  battery,  B,  through  the  wire, 
MN,  is  now  such  that  it  causes  between  1,434  of  the  2,000  spaces 
in  which  that  wire  is  divided,  a  drop  of  potential  of  1.434 
volts,  the  difference  in  potential  between  M  and  N  is  evidently 
two  volts.  If  therefore  the  switch,  D,  is  thrown  over,  so  as 
to  apply  to  the  points,  M  and  <7,  an  unknown  potential,  which 


POTENTIOMETERS. 


75 


must,  of  course,  be  less  than  two  volts,  and  the  contact,  (?,  is 
moved  along  the  wire  until  the  galvanometer  shows  no  deflec- 
tion, the  E.M.F.  of  the  source  to  be  measured  is  given  directly 
by  a  number  of  the  divisions  between  M  and  (?,  each  of  which 
divisions  represents  .001  volt. 

In  actual  practice  the  length  of  the  wire,  MN,  is  usually 
made  about  one  meter.  If  it  is  longer  the  apparatus  becomes 
awkward  to  handle,  and  if  much  shorter  it  is  extremely  diffi- 
cult to  read  its  scale,  with  2,000  divisions,  without  straining  the 
eyes. 

A  more  practical  form  of  potentiometer  is  diagrammatically 
shown  in  Fig.  51.  It  will  be  noticed  that  this  differs  from  the  ele- 
mentary one  in  that  the  resistence  between  the  points  M  and  JVis 


FIG.  51. 

no  longer  composed  of  a  single  straight  wire,  but  of  fourteen  coils 
of  wire,  each  provided  with  an  appropriate  terminal,  plus  the 
straight  wire.  The  resistance  of  each  of  the  coils  is  the  same 
as  that  of  the  straight  wire,  MN' ,  and  both  of  the  wires  running 
to  the  multithrow  switch  terminate  in  contacts  which  may  be 
moved  along  the  resistance,  MN.  In  this  form,  if  the  rheostat 
R,  be  adjusted  so  that  the  difference  of  potential  between  M 
and  N is  1.5  volts,  the  fall  of  potential  between  the  terminals  of 
each  of  the  fourteen  coils  is  one  tenth  of  a  volt,  and  if  the  wire, 
MN,  be  divided  into  1,000  divisions,  the  difference  of  poten- 
tial between  each  will  be  YoJo"o  °f  a  volt;  in  other  words,  the 
arrangement  is  made  ten  times  as  sensitive  as  the  elemen- 


76         ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

tary  form  by  the  addition  of  supplementary  coils.  The  length 
of  the  wire,  MN7,  may  be  made  somewhat  less  than  a  meter,  but 
if  the  apparatus  is  to  be  used  for  considerable  periods  at  a  time, 
the  length  should  not  be  less  than  two  feet,  because  of  the  strain 
on  the  eyes  of  the  observer,  due  to  the  fineness  of  the  divisions. 
The  modified  form  has  an  additional  advantage  over  the  ele- 
mentary, in  that  the  resistance  between  the  points  M  and  N  is 
far  higher,  and  there  is  therefore  less  current  drawn  from  the 
battery  B,  with  a  consequent  less  liability  of  change  in  strength 
of  that  current.  In  both  it  is  essential  that  the  straight  wire  be 
of  uniform  resistance  throughout  its  length,  in  order  that  the 
drops  across  equal  portions  thereof  may  be  uniform. 

Calibration  of  the  Slide  Wire. 

As  the  accuracy  of  a  slide  wire  potentiometer  depends  funda- 
mentally on  the  assumption  that  the  wire  is  of  uniform  resistance 
throughout  its  length,  and  as  the  results  given  by  it  are  erone- 
ous  unless  this  holds  rigorously  correct,  it  is  well  that  a  user 
should  know  how  to  investigate  this  point  for  himself. 

Accurate  checking  is  at  best  a  tedious  process,  the  following 
being  probably  the  most  convenient  method  :  First,  two  stand- 
ard resistance  coils  of  a  value  which  may  conveniently  be  in  the 
neighborhood  of  one  ohm  each  are  selected,  and  these  must  then 
be  adjusted  so  that  their  resistances  are  exactly  alike.  This  is 
usually  accomplished  by  shunting  the  higher  resistance  one 
with  a  plug  resistance  box  and  altering  the  box  resistance  until 
the  two  are  shown  by  any  convenient  one  of  the  methods  de- 
scribed in  the  chapter  on  resistance  measurements  to  be  exactly 
the  same.  That  fine  adjustments  are  possible  in  this  manner  is 
evident  from  consideration  of  the  fact  that  if  the  box  has  a 
resistance  of  as  low  as  say  2,000  ohms,  and  this  is  placed  in 

1  x  2000 
shunt  to  one  ohm,  the  combined  resistance  becomes 


ohms,  or  approximately,  .9995  ohms,  a  variation  of  .05  per  cent. 
Having  by  such  means  obtained  two  exactly  equal  resistances, 
adjust  one  of  them  so  that  its  resistance  differs  from  that  of  the 
other  by  a  very  small  but  definite  amount,  which  it  may  be 
assumed  is  obtained  by  shunting  it  with  1,000  ohms.  If  each 
of  the  resistances  were  originally  x  ohms,  the  one  shunted  by 


POTENTIOMETERS. 


77 


1,000  ohms  becomes  -JTTTJTJ and  the  difference  between  them, 

x —    ^.         -  ohms.      The   two   coils  differing  by  the  known 
J.UUU  -]- X 

amount,  derived  from  the  above  formula,  are  then  used  as  the 
coils  A  and  Bin  the  arrangement  shown  in  Fig.  52,  which  figure 
will  be  understood  to  be  merely  diagrammatic.  In  the  same 
figure  ab  form  the  terminals  to  which  the  extremities  of  the 
wire  under  test  are  secured  and  e  and/,  terminals  for  another 
bare  stretched  wire,  whose  resistance  per  unit  of  length  need, 
however,  not  be  uniform.  A  battery  and  a  galvanometer  are 
also  provided  as  shown.  The  galvanometer  contact  G-  is  now 
moved  along  the  wire  ef,  until  the  galvanometer  shows  no  de- 
flection, with  the  contact  Q  kept  constantly  at  position  1 ;  this 
point  is  noted,  and  the  coils  A  and  B  interchanged.  The  gal- 


vanometer  can  again  be  brought  back  to  zero  by  moving  C  to  the 
point  2.  The  distance  between  the  points  1  and  2  of  the  wire 
under  test  is  then  the  difference  of  the  resistance  of  the  coils 
A  and  B.  The  coils  A  and  B  are  now  put  back  in  their  origi- 
nal positions,  and  0  being  kept  at  the  point  2,  the  contact  6r 
shifted  to  another  position,  6rr,  on  the  wire  ef,  where  balance 
is  restored.  This  evidently  forms  a  fresh  starting  point,  and 
the  resistance  of  the  section  2-3  of  the  wire  under  test  may  be 
found  in  terms  of  the  difference  between  the  resistances  A  and 
B.  The  process  is  repeated  until  the  whole  wire  ab  has  been 
divided  up  into  sections  of  equal  and  known  resistance.  If 
these  coincide  with  the  scale  markings  on  the  potentiometer  as 
secured  from  the  maker,  it  may  safely  be  presumed  that  the  wire 


78         ELECTRIC   AND  MAGNETIC  MEASUREMENTS. 

has  been  properly  tested  for  and  adjusted  to  uniformity,  or  else 
that  the  scale  has  been  drawn  to  allow  for  inequalities  in  the 
wire. 

When  calibrating  a  wire  that  has  not  been  checked  before,  it 
is  usually  advisable  to  make  the  above  test  more  than  once, 
using  fresh  values  of  difference  in  resistance  between  A  and  J9, 
in  order  that  the  measurements  will  include  practically  every 
section  of  the  wire  length. 

A  rougher  test  of  the  uniformity  of  resistance  of  a  slide  wire 
may  be  made  by  passing  a  continuous  current  of  an  appropriate 
constant  strength  through  it  and  then  by  means  of  a  pair  of 
contacts  held  rigidly  spaced  at  a  small  distance  apart,  observ- 
ing whether  the  deflections  of  a  galvanometer  attached  to  the 
contact  terminals  are  the  same  wherever  on  the  wire  length  the 
contact  may  be  applied.  If  they  are,  the  wire  is  ^evidently 
electrically  uniform. 

Contact  Devices. 

The  device  used  to  make  contact  with  a  potentiometer  wire 
must  be  carefully  constructed  in  order  that  its  position  with 
reference  to  the  fixed  scale  may  be  accurately  read  off  and  that 
the  operator  cannot  mar  the  wire  when  making  contact,  and  thus 
destroy  the  uniformity  of  its  resistance.  The  form  of  contact 
used  in  the  old  model  Crompton  potentiometer,  which  instrument 
is  built  on  the  principle  illustrated  by  Fig.  51,  is  illustrated  in 

Fig.  53.  Here  S  is  the  extremity 
of  a  long  weak  spring,  which 
tends  to  press  downward  the 
wedge-shaped  block  secured  to 
the  end  of  the  spring.  The  down- 
ward tendency  of  S  is  more  than 
FIG.  53.  overbalanced  by  the  upward  pull 

on  it  exerted  by  the  button-shaped  head  of  the  plunger, 
P,  beneath  whose  shoulder  there  abuts  a  spiral  spring.  P  is 
the  knob  that  is  depressed  by  the  operator  when  it  is  desired 
to  make  contact  with  the  wire  and  the  exertion  of  considerable 
pressure  on  the  knob,  P,  will  not  increase  the  pressure  of  the 
contact  on  the  wire,  as  P  simply  releases  the  weak  spring  that 
carries  S,  and  the  pressure  on  the  wire  is  determined  solely  by 
the  elasticity  of  that  spring.  The  knurled-headed  screw  pro- 


POTENTIOMETERS. 


79 


jecting  from  the  end  of  the  contrivance  works  a  micrometer 
screw  to  make  very  fine  adjustments.  An  even  more  elaborate 
form  of  contact  is  shown  in  Figs.  54  and  55,  this  being  one 
designed  by  Callender  and  Griffiths  for  use  with  their  labora- 
tory standard  bridges.  It  is  made  in  two  parts,  one  of  them, 
ABA',  sliding  against  the  non-graduated  guide  bar  that  is 
placed  parallel  to  the  graduated  scale,  and  the  other  against  the 
graduated  bar.  The  first  part  is  steadied  by  means  of  springs, 
placed  as  shown,  that  keep  it  in  contact  with  its  guide,  and  the 
second  piece  in  a  similar  manner  has  a  flat  spring  between  it 
and  the  first.  To  the  section  ABA'  is  attached  a  bracket 
carrying  the  screw  S,  which  is  used  to  make  fine  adjustments. 
When  this  is  turned,  the  inner  block,  E,  alone  moves,  as  its 
pressure  against  the  graduated  bar  is  only  that  due  to  the  spring 
at  EE',  whereas  the  pressure  of  the  outer  portion  against  the 
guide  bar  on  which  it  slides  is  the  pressure  exerted  by  the 
spring  EE',  plus  that  of  the  springs  at  AA'.  The  wire,  W, 


FIG.  54. 


FIG.  55. 


is  brought  into  contact  with  the  sliding  wire  itself,  and  the  one 
parallel  to  it  attached  to  the  galvanometer  terminal  by  turning 
the  screw,  O,  and  forcing  the  slide  and  galvanometer  wires  down 
on  one  running  at  right  angles  thereto.  By  this  means  a  very 
definite  point  of  contact  may  be  obtained.  It  is  very  difficult 
for  a  careless  operator  to  injure  the  potentiometer  wire  with 
this  form  of  bridge,  for  if  it  were  attempted  to  move  it 
without  releasing  the  screw,  O,  the  outer  block,  ABA',  would 
simply  move  relative  to  the  inner  one  without  tearing  or  deform- 
ing the  wire. 

In  commercial  potentiometers  where  laboratory  accuracy  is 
not  required  and  the  item  of  cost  comes  into  consideration,  it  is 
becoming  more  common  practice  to  use  a  simpler  form  of  con- 
tact in  connection  with  the  slide  wire.  This  device  is  continu- 
ally in  contact  with  the  wire,  and  is  simply  slid  along  from  one 
position  to  the  other  when  readings  are  being  made.  Such  con- 


80       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


tacts  usually  take  the  form  of  rather  blunted  knife  edges  at 
right  angles  to  the  wire  length,  being  pressed  against  the  slide 
wire  by  a  weak  spring  and  supported  by  a  rigidly  guided  block. 
The  spring  tension  must  be  adjusted  with  great  care  to  avoid 
the  wear  on  the  slide  wire  that  would  ensue  if  it  were  too  great, 
and  the  uncertain  contact  that  would  exist  if  it  were  too  small. 
The  spring  adjustment  is  usually  fixed  by  the  maker  of  the  in- 
strument and  no  means  are  provided  by  which  the  user  can 
change  it  later  on. 

With  the  constantly  engaged  form  of  contact  it  is  necessary  to 
be  particularly  careful  to  see  that  both  the  wire  and  contact  are 


OAQ       O»O       OcQ 


FIG.  56. 


perfectly  clean,  as  any  grit  would  cause  rapid  and,  of  course,  un- 
even wear,  which  would  destroy  the  uniformity  of  the  resistance 
of  the  wire,  and  hence  the  accuracy  of  the  whole  device.  In  the 
present  type  of  the  Crompton  potentiometer,  which  is  probably 
the  best  known  of  the  slide-wire  type  instruments,  the  wire 
itself,  as  well  as  all  other  moving  contacts,  are,  as  is  shown  by 
Fig.  56,  completely  enclosed  and  shielded  by  plate  glass. 

In  one  form  of  the  Leeds  and  Northrup  instrument,  shown  in 
Fig.  57.  the  slide  wire  is  exposed  on  the  surface  of  the  marble 
drum  about  which  it  is  wound  in  a  manner  that  renders  it  easily 


POTENTIOMETERS. 


81 


accessible  for  cleaning  with  a  soft  cloth,  or  fine  tissue  paper. 
In  both  instruments  it  is  necessary  to  keep  the  wire  coated  with 
a  thin  film  of  vaseline  or  parafrme  oil,  as  this  is  found  to  eliminate 
the  otherwise  troublesome  thermal  E.M.F's  set  up  at  the  point 
of  contact  and,  of  course,  diminishes  the  wear. 

In  a  later  design  of  the  Leeds  and  Northrup  potentiometer, 
the  marble  drum  is  covered  by  a  cylindrical  shield  to  protect  it 
from  dust. 


All    potentiometers    of    the    slide-wire    type   are    somewhat 
objectionable  in  that  their  necessarily  low  resistance  means  that 


FIG.  57. 


a  fairly  heavy  current  is  required  from  the  working  battery,  a 
condition  that  involves  more  rapid  polarization  with  a  conse- 
quent change  in  the  drop  along  the  wire.  To  check  up  the  cor- 
respondence  of  the  wire  and  its  scale  is  further,  as  is  evident 
from  what  has  before  been  said,  an  extremely  tedious  operation, 
and  one  calling  for  auxiliary  apparatus  of  a  kind  that  is  not 
always  available.  On  the  other  hand,  the  low  resistance  poten- 
tiometer is  better  suited  for  making  measurements  of  very  small 
potentials,  and  being  continuously  adjustable,  has  an  infinite 
number  of  steps  in  contrast  to  any  step  by  step  design. 


82        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 
RESISTANCE   COIL   POTENTIOMETERS. 

Potentiometers  having  a  relatively  high  resistance  may  be 
made  by  substituting  for  a  straight  wire  a  set  of  resistance  coils 
electrically  connected  in  series,  and  with  their  terminals  attached 
to  contact  plates  or  buttons. 

If  it  be  desired  to  work  to  the  fourth  or  fifth  decimal  place 
the  number  of  coils  that  would  be  required,  if  a  separate  one 
were  provided  for  each  step,  would  be  prohibitively  large,  one 
thousand,  for  instance,  being  needed  to  replace  the  slide  wire 
alone  if  the  wire  scale  of  the  Crompton  instrument  was  to  be 
duplicated. 

To  avoid  this  a  modification  of  the  Varley  slide,  which  is 
analogous  to  the  vernier  used  in  mechanical  measurements,  is 
used.  Referring  to  Fig.  58,  in  which  the  apparatus  is  diagram- 
matically  illustrated,  between  the  points  A  and  C  tbfere  are 


—  —  .10,  10  Ohm  Coils:  —  —  • 
\ 


FIG.  58. 

fourteen  coils,  each  of  1,000  ohms  resistance,  connected  to  the 
terminal  contacts  shown.  Between  the  points  0  and  J5,  10 
resistances  of  10  ohms  each  are  similarly  connected.  Between 
E  and  F  there  are  9  coils,  each  of  1,000  ohms  resistance,  and 
between  G-  and  H,  9  coils,  each  of  10  ohms  resistance.  The 
terminals  of  EF  and  Grff  are  connected  to  a  pair  of  contact 
points,  3£M~ and  MfMf,  respectively,  rigidly  coupled  together  by 
means  of  an  insulating  piece,  and  held  separated  by  a  distance 
equal  to  the  space  between  the  contact  buttons  of  the  coils  com- 
posing A  C  and  CB  respectively.  Referring  first  to  section  A  O 
of  the  apparatus,  the  drop  of  potential  between  the  buttons 
under  MM  is  evidently  that  due  to  the  flow  of  the  current 
through  a  circuit  composed  of  1,000  ohms  resistance  shunted 
by  9,000  ohms,  namely,  a  circuit  of 

9000x1000 


POTENTIOMETERS.  83 

As  this  drop  is  that  between  j^and  F,  which  in  turn  is  com- 
posed of  a  series  of  nine  equal  resistances,  the  drop  between 
any  two  buttons  on  EF  is  evidently  that  due  to  the  cur- 
rent flowing  through  a  resistance  of  one  ninth  of  900  ohms, 
namely,  100  ohms.  In  an  exactly  similar  way  the  drop  be- 
tween the  contact  buttons  of  the  resistance  forming  the  series 
GrH,  is  that  due  to  the  current  flowing  through  1  ohm.  In 
other  words,  if  adjustable  contacts  be  made  to  slide  over  EF 
and  GrH,  the  total  drop  may  be  varied  in  four  steps,  the  unity 
steps  being  caused  by  shifting  the  contact,  1,  along  GrH,  the  tens 
steps  by  shifting  MM  along  GB,  the  hundreds  steps  by  shifting 
J  along  EF,  and,  finally,  the  thousands  steps,  by  shifting  MM 
along  AC.  The  total  range  is  made  to  take  in  1,500  units  in 
order  that  the  value  of  the  E.M.F.  of  the  standard  cell  to  be 
used  for  comparison  'purposes  may  be  set  off  directly  to  steps 
corresponding  to  a  resistance  of  1,434  ohms  if  the  Clark  cell  is 
used,  or  1,019  ohms  if  the  Weston  cell  is  used,  whereupon  any 
E.M.F.  to  be  measured  in  terms  of  the  standard  cell  could  be  read 
directly  by  steps  of  .0001  volt  each. 

The  resistance  of  the  contracts  at  MM,  M'M',  J,  and  I  intro- 
duce errors  that  are  inappreciable.  Taking,  for  instance,  the 
case  of  the  contacts  M'M',  if  these  had  a  resistance  as  high  as 
0.1  ohm,  the  10-ohm  coil,  to  whose  terminals  connection  is  made, 
is  shunted  by  90.1  ohms  instead  of  90  ohms,  and  the  resultant 

resistance  is  -^ —     — —  =  9.001  ohms  instead  of  9  ohms,  which 

10  +  903 
is  an  error  of  only  about  .01  of  1  per  cent. 

As  the  resistance  coils  entering  into  the  construction  of  this 
type  of  potentiometer  are  all  of  either  ten  or  one  thousand  ohms 
value,  it  is  a  very  simple  matter  to  check  the  adjustment  at  any 
time  as  almost  every  testing  installation  includes  apparatus  by 
means  of  which  resistances  of  this  order  may  be  compared  with 
a  high  degree  of  accuracy.  Each  contact  button  usually  has  a 
hole  drilled  in  it  at  some  convenient  point  and  is  provided  with 
a  set  screw,  so  that  it  is  easy  to  attach  wires  to  the  terminal  of 
each  individual  coil  to  measure  its  resistance. 

It  should  be  noted  that  it  is  not  essential  even  that  standard 
resistances  of  10  and  1,000  ohms  respectively,  be  available,  as  all 
that  is  necessary  in  order  to  have  the  apparatus  read  correctly 


84        ELECTRIC   AND    MAGNETIC  MEASUREMENTS. 

is  that  all  the  1,000  ohm  resistances  shall  be  alike  and  all  the  10 
ohm,  resistances  alike,  and  equal  to  one  one-hundredth  part  of 
the  nominal  1,000  ohm  resistances.  Any  one  of  the  coils  may, 
therefore  be  used  as  the  standard  of  comparison,  and  if  the  others 
agree  with  it  the  apparatus  is  in  proper  shape. 

Leeds  and  Nbrthrup  Potentiometer. 

A  potentiometer  of  the  step  by  step  type  using  the  Varley 
slide,  is  shown  in  plan  view  in  Fig.  59,  the  connections  of  the 
same  being  illustrated  by  Fig.  60.  It  will  be  observed  that  the 
series  of  coils  in  the  right-hand  side  of  the  figure,  that  is  to  say, 
between  0  and  B,  is  provided  with  a  slide  on  a  slide,  thus  in- 


FIG.  59. 


creasing  the  number  of  readable  steps  to  15,000.  A  feature  of 
great  convenience  in  this  potentiometer  is  the  arrangement  for 
throwing  in  the  standard  cell  for  making  the  initial  adjustment 
of  the  rheostat  R  in  the  working  cell  circuit  and  of  allowing  the 
checking  at  any  instant  of  the  fact  that  the  current  sent  through 
the  potentiometer  by  the  working  cell  has  remained  unchanged, 
both  without  necessitating  a  resetting  of  the  five  radial  switch 
arms  to  the  positions  corresponding  to  the  standard  cell  voltage. 
This  is  accomplished  as  follows  :  In  Fig.  60  the  resistance 
of  the  fifteen  1,000-ohm  coils  between  A  and  (7,  one  of  which 
is  always  shunted  by  9,000  ohms,  is  14,900  ohms,  and  of  the 
ten  10-ohm  coils  in  CB,  as  shunted  by  the  double  slides,  99.9 
ohms,  a  total  of  14999.9  ohms. 


POTENTIOMETERS. 


85 


Now,  assuming  that  a  non-saturated  solution  Clark  cell  is  to 
be  used  as  the  standard,  the  maximum  temperature  at  which 
this  will  be  employed  would  hardly  exceed  32°  C.,  at  which 
point  its  E.M.F.  would  be,  according  to  the  formula  before 
given,  1.4355  volts. 

Now,  if  the  standard  cell  were  at  E  and  the  double  pole- 
switch  £7  in  the  position  shown,  the  various  slides  would  have 
to  be  set  to  positions  making  the  drop  at  the  cell  terminals,  that 
is,  across  14,355  ohms,  in  order  that  when  the  working  cell  cur- 
rent was  adjusted  by  the  rheostat,  R,  so  that  there  would  be  no 


FIG.  60. 


deflection  of  the  galvanometer,  G-,  when  the  key,  FJ  was  closed, 
the  drop  per  readable  point  on  the  potentiometer  should  be 
exactly  .0001  volt. 

By  simply  shifting  the  double  pole-switch,  Z7,  to  its  other 
position,  however,  it  will  be  seen  that  no  matter  where  the 
slides  may  be  placed  (with  a  single  exception  to  be  noted 
presently)  the  resistance  across  which  the  cell  terminals  is 
connected  is  AC  (13,900  ohms),  plus  CB  (99.8  ohms),  plus  K, 
which  latter  is  made  355.1  ohms,  a  total  of  14,335  ohms,  or 
just  what  is  required.  To  allow  for  the  increased  E.M.F.  of 


86        ELECTRIC  AND  MAGENTIC  MEASUREMENTS. 

the  standard  cell  with  decreasing  temperatures,  the  series  of 
coils  between  T  and  S  is  added,  the  value  of  each  coil  being 
made  such  that  when  the  plug  shown  in  the  diagram  as  at  Tis 
shifted  to  another  position,  stamped  as  shown  in  Fig.  59,  with 
the  different  temperatures  that  the  cell  may  have,  the  total 
resistance  between  the  terminals  of  S  is  added  to  sufficiently 
to  effect  the  necessary  compensation. 

The  one  position  of  the  slides  at  which  the  resistance  of  the 
series  AC  is  not  13,900  ohms,  is  when  the  slide  for  that  series 
spans  the  first  coil,  Aa.  To  avoid  its  being  necessary  for  the 
operator  to  make  inspection  each  time  to  see  that  the  slide  is  not 
in  that  position  when  making  a  standard  cell  setting  or  check, 
the  coil  ac  is  divided  into  two  sections,  ab  of  100  ohms,  and  be 
of  900  ohms.  The  small  single  pole-switch  shown  at  that  point 
and  clearly  illustrated  also  in  Fig.  59  is  mechanically  interlocked 
with  the  slide  arm  lever  in  such  a  manner  that  when  the  latter 
is  at  the  position  Aa  it  connects  the  standard  cell  to  5,  and  when 
the  slide  is  at  any  other  position  it  connects  the  cell  to  a.  Of 
course,  when  the  standard  cell  is  of  a  type  having  some  voltage 
other  than  that  of  the  non-saturated  solution  (Clark)  the  value 
of  the  resistance  at  K,  and,  if  necessary,  the  point  of  attach- 
ment of  #,  is  appropriately  changed  at  the  time  that  the  appara- 
tus is  built.  If  the  cell  has  no  temperature  coefficient,  the 
coils  TS  are  omitted. 

Other  potentiometer  constructions  which  maintain  a  constant 
resistance  of  the  working  cell  circuit  and  at  the  same  time 
allow  a  shifting  of  the  points  at  which  contact  may  be  made 
along  that  circuit  are  feasible,  and,  in  fact,  in  some  use,  but  'the 
two  above  described  are  the  most  common  and  the  best  suited 
to  ordinary  requirements. 

Before  leaving  the  general  subject  of  the  potentiometer 
method  of  measurement,  it  may  be  well  to  point  out  that  one 
reason  for  the  great  accuracy  attainable  thereby  is  that  it  is 
a  zero  method,  that  is  to  say,  the  results  are  obtained  when  a 
galvanometer  shows  an  absence  of  current  rather  than  when 
it  gives  a  certain  deflection.  In  this  way  errors  due  to  varia- 
tions of  magnetic  force  when  measurement  is  going  on,  to 
alterations  in  resistance  of  the  galvanometer  circuit  because  of 
temperature  changes,  to  an  alteration  in  the  restoring  force 


POTENTIOMETERS.  87 

of  the  galvanometer  system,  to  a  change  in  potential  of  the 
standard  cell  due  to  drawing  too  great  a  current  from  it,  and  to 
varying  contact  resistances,  are  all  eliminated. 

The  Lorenz  apparatus  for  the  determination  of  resistance  in 
terms  of  the  fundamental  units,  as  described  on  page  6,  is 
an  example  of  the  potentiometer  system  of  measurement  as 
is  likewise  the  method  of  plotting  the  wave  forms  of  alternating 
currents  described  on  page  259.  Other  applications  are 
numerous. 

MEASUREMENT    OF  E.M.F.  WITH   A   POTENTIOMETER. 

The  method  of  measuring  the  difference  of  potential  between 
any  two  conductors  led  to  a  potentiometer  is  fairly  obvious 
from  the  foregoing  descriptions  of  this  class  of  apparatus. 
The  procedure  involves,  first,  the  establishment  of  a  known 
difference  of  potential  per  step,  if  the  potentiometer  is  of  the 
step  by  step  type,  or  per  scale  division,  if  of  the  slide  wire  type, 
by  adjusting  the  strength  of  the  current  supplied  by  the  work- 
ing cell  until  the  standard  cell  voltage  is  exactly  balanced  by 
the  drop  over  the  number  of  steps  or  divisions  equal  to  its 
voltage. 

The  unknown  E.M.F.  is  then  applied  to  the  series  of  resist- 
ances by  manipulating  the  sliding  contacts  until  a  point  is 
found  where  no  current  flows  through  that  branch  circuit, 
whereupon  it  is  known  that  the  difference  of  potential  between 
the  ends  of  the  circuit  is  the  same  as  that  existing  across  that 
number  of  steps  of  the  potentiometer. 

Volt  Boxes. 

It  is  obvious  that  none  of  the  potentiometers  so  far  described 
is  suitable  for  the  measurement  of  potentials  in  excess  of  1.5  or 
2  volts.  To  measure  higher  ones,  devices  called  "  volt  boxes  " 
are  used,  which  are  simply  coils  of  wire  of  high  resistance  hav- 
ing terminals  attached  so  that  one  half,  one  tenth,  one  one-hun- 
dredth, or  any  other  desired  fraction  of  the  total  E.M.F.  between 
the  volt-box  terminals  exists  between  the  one  end  of  the  volt 
coil  and  the  lead  selected.  Where  the  potentiometer  is  to  be 
used  to  cover  a  wide  range  of  measurement,  the  volt  box  is 
made  to  contain  several  coils,  often  having  a  resistance  of  50, 


88        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

50,400  and  9,500  ohms  respectively,  connected  in  series  as 
shown  in  Fig.  61.  From  this  figure  it  is  evident  that  if  the 
leads  to  the  potentiometer  be  attached  at  a  and  6,  a  difference 
of  potential  as  high  as  300  volts  may  exist  between  a  and  e  with- 
out making  the  E.M.F.  applied  to  the  instrument  come  above  its 
maximum  capacity  of  1.5  volts,  in  other  words,  the  volt  box  is  at 
that  step  a  multiplier  of  200.  If  the  potentiometer  connection 
be  made  at  a  and  c  the  potential  difference  between  a  and  e  may 
be  as  high  as  150  volts  without  exceeding  the  potentiometer's 
capacity,  and  the  volt  box  acts  as  a  multiplier  of  100 ;  similarly, 
the  step  ad  forms  a  multiplier  of  20,  permitting  the  measure- 
ment of  potentials  up  to  30  volts. 

When  the  voltage  to  be  measured  is  over  1.5  and  less  than  3 
volts,  the  range  of  the  potentiometer  itself  may  be  temporarily 

Applied     E.M.F 
50 a)       50  a)  400 a}  95OO  a> 

(VWVK^A/V^^ 

<*>          '6          \c  \d,  |c 

1  I 

J 


.__  TO   Potentiometer 

FIG.  61. 

doubled  by  using  two  standard  cells  in  series  instead  of  one,  and 
two  working  cells  in  series  instead  of  one,  the  value  of  the 
potential  difference  per  scale  division  being  thus  doubled.  This, 
however,  means  the  passage  of  a  current  of  twice  the  normal 
strength  through  the  potentiometer,  and  it  should  first  be  ascer- 
tained whether  the  device  can  safely  withstand  that  overload. 

CURRENT   MEASUREMENTS   WITH   THE   POTENTIOMETER. 

Currents  are  measured  with  the  aid  of  the  potentiometer  by 
determining,  in  terms  of  the  E.M.F.  of  a  standard  cell  as  usual, 
the  drop  in  potential  across  a  known  standard  resistance, 
traversed  by  the  current  whose  strength  is  to  be  ascertained,  and 
then  calculating  the  current  from  Ohm's  law.  Such  standard 


PO  TEN  TIOMETERS. 


89 


resistances  must,  of  course,  be  selected  to  have  a  value  which 
will  give  a  sufficiently  large  drop  when  traversed  by  the  cur- 
rent to  enable  this  to  be  accurately  read,  and  must  also  have  a 
section  large  enough  to  carry  that  current  for  a  sufficient  time 
to  make  the  test,  without  heating  to  an  extent  that  appreciably 
increases  the  resistance. 

While  such  standard  low  resistances,  or  shunts,  as  they  are 
sometimes  called,  are  usually  purchased  by  a  user  as  a  finished 
piece  of  apparatus,  it  may  not  be  out  of  place  to  point  out  some 
of  the  precautions  that  must  be  observed  in  their  proper  design, 
as  these  have  some  bearing  on  their  use.  Moreover,  it  is  some- 
times desirable  to  extemporize  a  shunt,  as  can  readily  be  done 
by  taking  a  suitable  resistance  and  calibrating  it  by  measuring 
its  value  in  terms  of  any  of  the  sizes  of  shunts  already  on  hand 


i    / 


i    I 


y/'/li  j 

\ 
j 

i    '    /   /   / 
i    ////,' 

'//I! 

d 

i 
j 
I 

•  i    '   /  /  /  / 

*  !,'////: 

i  ,  j  i  i  f  /  /  ,'-. 

D 


V  \  \  *  '  >  ' 

=£M  \  j  i  i  i 

:»Yjij    1 1  1. 1 

-',''\\\  \d\ 

'//I  I  j  I 


i    ; 

y 
ji 

j! 

w 
i  j 

FIG.  62. 


by  the  potentiometer  resistance  measuring  method  to  be  de- 
scribed presently,  and  in  that  case  a  failure  to  observe  the  pre- 
cautions is  apt  to  make  the  results  inaccurate. 

Standard  Low  Resistances. 

Standard  low  resistances,  then,  may  not  consist  of  a  simple 
sheet  of  resistance  metal  through  which  the  current  to  be 
measured  is  passed  and  between  any  two  equidistant  points  on 
which  the  drop  is  taken,  unless  the  points  of  attachment  of  the 
main  and  potential  wires  are  always  the  same.  This  is  because 
the  current  flowing  through  a  sheet  will  distribute  itself  differ- 
ently with  different  points  of  attachment  of  the  terminal  wires. 
Fig.  62  illustrates  this  point.  Here  A  is  a  resistance  sheet 
into  which  the  current  is  lead  by  a  terminal,  a,  secured  to  the 


90         ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

upper  left-hand  corner,  and  out  again  through  the  upper  right- 
hand  corner,  b.  B  shows  the  same  plate  with  the  current  led 
in  and  out  through  diagonally  opposite  corners,  and  (7,  the  same 
thing  again,  but  with  the  current  conducted  through  it  by  con- 
ductors attached  to  the  center  of  the  plate  at  each  end.  The 
curves  in  the  figures  are  lines  connecting  the  points  of  equal 
potential  as  found  by  actual  measurement  with  a  galvanometer 
and  exploring  points,  and  are  credited  by  Mr.  Fisher  to  Mr.  A. 
C.  Keep.  The  author  has  made  similar  tests  which  substantiate 
these.  The  proper  current  distribution  in  the  plate  is  attained 
only  by  working  along  the  lines  shown  in  D  of  the  same  figure, 
where  there  are  heavy  terminal  blocks,  either  of  another  mate- 
rial than  the  resistance  sheet,  or  else  heavy  masses  of  the  .same 
material.  Even  with  this  form  care  must  be  taken  in  propor- 
tioning the  terminals,  for  if  their  size  be  insufficient  or^  the  re- 
sistance of  the  attached  lugs  too  high,  the  distribution  may  be 
affected  to  an  appreciable  degree. 

Another  important  consideration  is  the  location  of  the  con- 
tact points  where  attachment  is  made  to  the  potentiometer  or 
other  apparatus  for  measuring  the  drop  due  to  the  current  flow. 
In  shunts  for  commercial  indicating  instruments  where  the 
highest  accuracy  is  not  required,  it  is  not  uncommon  to  attach 
these  drop  studs  to  the  terminal  blocks,  as  by  this  means  a 
maximum  drop  is  obtained  and  a  saving  in  material  is  effected. 
This  location  is  not  only  apt  to  bring  the  drop  studs  to  a 
position  where  the  equipotential  lines  are  disturbed  when  cur- 
rent is  led  into  and  out  of  the  terminal  blocks  at  different  angles 
but  to  introduce  thermoelectric  potentials,  which,  whether  they 
be  opposing  or  assisting  the  drop  due  to  the  current,  of  course 
introduce  errors.  These  foreign  potentials  are  generated  for 
the  following  reasons.  The  material  of  the  resistance  strip  is 
ordinarily  different  from  that  of  the  terminal  blocks,  the  latter 
being  usually  of  copper  and  the  former  of  some  resistance  alloy 
like  manganin  or  German  silver.  If  the  temperature  at  the 
junction  between  the  resistance  plate  and  one  terminal  lug  be  the 
same  as  that  at  the  junction  between  the  plate  and  the  other  lug, 
the  thermoelectric  E.M.F.  between  one  of  them  and  the  resis- 
tance sheet  is  equal  and  opposite  to  that  between  the  resistance 
sheet  and  the  other  lug,  and  hence  there  is  no  difference  of 
potential  between  the  contact  points  on  the  lugs  due  to  that 


POTENTIOMETERS.  91 

source.  If,  however,  as  is  often  the  case,  one  of  the  junctions 
be  hotter  than  the  other,  due,  perhaps,  to  imperfect  soldering 
between  the  resistance  sheet  and  the  lug,  or  perhaps  to  a  poor 
contact  between  the  lug  and  the  wire  which  carries  the  current, 
the  heat  generated  thereby  being  conducted  by  the  lug  to  the 
junction  generates  an  E.M.F.  The  potential  between  the  sheet 
and  one  lug  becomes,  therefore,  greater  than  that  between  the 
sheet  and  the  other  lug,  and  the  algebraic  sum  of  these  poten- 
tials, namely,  their  arithmetical  difference,  represents  a  foreign 
difference  of  potential  that  will  exist  between  the  points  of 
attachment  of  the  measuring  instrument. 

The  author  has  known  of  instances  in  which  these  potentials 
amounted  to  fully  5  per  cent  of  the  difference  in  potential 
between  the  drop  studs,  due  to  the  full  capacity  current  flow. 
The  objection  can  be  overcome  by  the  simple  expedient  of  at- 
taching the  drop  stud  to  the  resistance  sheet,  as  indicated  at  6?, 
Fig.  62,  instead  of  the  outer  lugs.  This  is  at  the  expense  of 
increased  weight  and  bulk,  but  safeguards  against  errors  that 
are  large  enough  to  be  objectionable  when  making  measure- 
ments of  any  accuracy. 

RESISTANCE  MEASUREMENT  WITH  A  POTENTIOMETER. 

The  method  of  comparing  resistances  with  the  aid  of  a  potentio- 
meter is  very  simple  ;  it  consists  of  coupling  together  in  series 
a  standard  resistance  and  the  one  under  test.  A  current  of 
suitable  strength  is  sent  through  these  resistances  and  the  drop 
in  potential  across  them  is  measured  by  means  of  the  potentio- 
meter. The  resistances,  since  the  current  in  both  is  the  same,  are, 
according  to  Ohm's  law,  in  direct  proportion  to  the  drops.  For 
such  resistance  work  it  is  very  desirable  that  the  multi-throw 
switch  of  the  potentiometer  be  provided  with  at  least  three  pairs 
of  contacts  for  making  connection  with  external  circuits,  one 
pair  being  for  standard  cell,  as  usual,  one  for  the  standard  resis- 
tance, and  the  third  for  the  unknown  resistance.  In  this  way  a 
simple  movement  of  the  switch  arm  throws  in  the  resistance  to  be 
measured,  while  the  drop  readings  may  be  taken  in  such  qnick 
succession  that  there  is  but  an  inappreciable  chance  of  any 
change  in  the  current  during  the  operation. 

This  system  of  resistance  measurement  is  capable  of  a  very 
high  degree  of  accuracy,  results  that  are  correct  within  one 


92         ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

part  in  1,000  being  attainable  with  very  ordinary  care.  When 
the  resistance  to  be  measured  is  of  a  very  different  order  from 
that  of  the  available  standard,  the  measurements  are  preferably 
made  indirectly,  by  lirst  constructing  a  secondary  standard  hav- 
ing a  value  of  one  tenth,  or  ten  times,  as  the  case  may  be,  of  that 
of  the  primary  one,  and  working  from  that,  or  even  a  tertiary 
standard  adjusted  from  it  in  a  similar  way.  Another  method 
of  accomplishing  the  same  end  consists  in  taking  the  drop  from 
the  unknown  standard  through  the  volt  box  already  mentioned, 
and  leading  only  a  fraction  thereof  to  the  potentiometer.  If, 
for  instance,  we  have  a  resistance  to  measure  approximately  .01 
ohm  in  value,  and  our  available  standard  is  1  ohm,  the  two 
may  be  joined  in  series  and  the  terminals  of  the  1  ohm  stand- 
ard connected  to  the  volt  box.  If,  then,  those  potentiometer 
terminals  of  the  volt  box  are  selected  that  give  the  ijatio  of 
one  one-hundredth,  the  drop  across  these  with  a  given  cur- 
rent flowing  through  the  standard  is  one  one-hundredth  of  the 
drop  across  the  terminals  of  the  standard  itself,  and  the  same 
as  the  drop  that  would  be  given  when  the  same  current  trav- 
ersed a  resistance  of  .01  ohm  value.  It  is  evident  that  tests 
made  as  above  are  best  suited  for  comparatively  low  resistance 
work. 


CHAPTER   V. 

THE  MEASUREMENT  OF  RESISTANCE. 

RESISTANCES  of  different  ohmic  value  must  be  measured  by 
using  different  tests  if  the  results  are  required  to  be  determined 
to  a  high  degree  of  accuracy.  While  there  is  no  hard  and  fast 
line  of  demarkation,  resistances  may  be  conveniently  divided  into 
three  groups,  namely,  medium  resistances,  this  including  those 
lying  between  .1  ohm  and  1  megohm  ;  low  resistances,  under  1 
ohm  ;  and  high  resistances,  over  1  megohm. 

Before  considering  the  various  methods  and  appliances  for 
resistance  measurements,  it  will  be  best  to  glance  briefly  at  the 
laws  determining  the  resistance  of  electrical  conductors  grouped 
in  various  combinations,  as  the  measurement  of  such  combina- 
tions or  networks  is  a  very  common  problem. 

When  we  have  several  conductors  connected  in  series  the  fact 
that  the  combined  resistance  of  all  is  the  sum  of  the  individual 
resistances  is  almost  axiomatic. 

When  the  conductors  are  connected  in  parallel  their  combined 
resistance  can  be  calculated  by  the  formula  derived  as  follows : 
Referring  to  Fig.  63  let  R^  be  a  conductor  having  a  resistance 
designated  by  Ml  and  R2  a  second  conductor  having  similarly  a 
resistance  R^  the  two  being  joined  in  parallel  as  shown ;  let  the 
current  through  Rl  be  designated  Jt  and  that  through  R^  by  1^ 
the  total  current  being  I.  According  to  Ohm's  law  we  now  have 

V  V 

Ji  =  J?   and  J2  =  75- » 

Rl  ^2 

V  being  the  difference  of  potential  between  the  junction  points 
A  and  B. 

Let  now  R  be  the  combined  resistance  of  the  two  conductors 
in  parallel,  that  is  to  say,  the  resistance  that  we  desire  to  ascer- 
tain. We  then  have 

. 

or  as  I  =  ^  4- 12, 

-=  —  +  —      or    i  =  -L+.l 
R     R^^     R^  R     RI     jR2 

93 


94 


ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


Where  more  than  two  conductors  are  connected  in  parallel, 
their  combined  resistance  may  be  ascertained  by  first  determin- 
ing the  resistance  of  one  pair  from,  the  above  formula,  finding 


the  combined  resistance  of  this  pair  and  the  next  succeeding 
conductor  by  substituting  the  value  of  the  pair  resistance  for 
that  of  a  simple  one,  and  so  on  throughout. 

As  all  systems  of  conductors  must  be  connected  either  in 
series  or  parallel,  or  combinations  of  the  two,  any  resistance  can 
be  calculated  if  that  of  its  elements  be  known,  by  the  application 
of  the  above  simple  principles.  However,  although  the  princi- 
ples themselves  are  very  simple,  their  practical  application  to 
networks  of  conductors  may  sometimes  involve  the  solution  of 
complicated  equations.* 

MEASUREMENT   OF   MEDIUM   RESISTANCES. 
THE  WHEATSTONE  BRIDGE. 

The  Wheatstone  bridge  is  a  network  of  six  conductors,  inter- 
connected as  shown  in  Fig.  64.  Four  of  them,  lettered  A,  B, 
0  and  X  respectively,  contain  resistances  only.  In  one  of  the 
remaining  branches  there  is  a  galvanometer,  and  in  the  other  a 


*  An  interesting  example  of  the  foregoing  is  the  calculation 
of  the  resistance  of  the  network  of  five  conductors  shown 
in  the  marginal  figure,  between  the  points  +  and  —  .  At  first 
glance  it  would  seem  as  if  this  should  be  given  by  a  simple 
expression,  but  actually  the  formula,  calculated  by  Townsend 
Wolcott  is  : 


(R 

• 


R  (R 


(R 

^ 


<Rb(Re+Rc}+Rd(Re+Rb) 
In  this  7?  is  the  total  resistance  and  R  with  subscript  letters,  the  resistances 
of  the  respectively  lettered  branches. 


THE  MEASUREMENT  OF  RESISTANCE. 


95 


source  of  current.  If,  with  all  the  connections  as  shown,  the 
galvanometer  gives  no  deflection,  its  terminals  are,  of  course, 
attached  to  points  in  the  network  which  are  at  the  same  poten- 
tial. In  these  circumstances,  if  A,  B,  C  and  X  represent  the 
resistances  of  the  conductors  whose  identity  they  respectively 
indicate,  the  relation  of  the  resistances  is  expressed  by  the 

equation,  _=  — .   This  may  be    demonstrated    as  follows:  It 
O       A 

is  obvious,  from  the  diagram,  that  the  current  is  divided  into 
two  branches ;  one  through  A  and  B,  the  other  through  C  and 
X.  Call  the  current  in  A  and  B,  I};  the  current  in  C  and  X, 


FIG.  64. 

I2.     By  hypothesis,  the  drop  over  A  equals  that  over   (7,  and 
the  drop  over  B  equals  that  over  X.     That  is, 

AIV  =  022  C1)    and    BIt  =  XI2  (2). 
Dividing  (1)  by  (2),  we  have, 

A      0  A       B 

^f.  =  -== ,    or    -^  =  — ,  as  stated. 
Jj       X  C        A 

From  the  last  equation  we  obtain, 

X  = 


When  this  condition  of  balance  exists,  the  conductors  containing 
the  battery  and  the  galvanometer  are  said  to  be  conjugate  ;  the 
battery  and  the  galvanometer  may  be  interchanged  and  the 
resistance  of  one  or  both  these  conductors  may  be  altered  with- 


96        ELECTRIC   AND  MAGNETIC  MEASUREMENTS. 


out  disturbing  the  balance.  This  is  a  most  important  fact,  and 
is  the  foundation  of  several  other  methods  of  testing. 

If  X  be  an  unknown  resistance,  and  the  resistance  of  O  and 
the  ratio  of  the  resistance  B  to  the  resistance  A  be  known,  then 
X  can  be  calculated.  The  fact  that  the  ratio  of  B  to  A  enters 
into  the  calculation,  makes  it  possible  to  cover  a  large  range  of 
measurement  with  a  comparatively  limited  range  of  the  adjust- 
able resistance,  C.  If,  for  instance,  B  and  A  be  equal,  the 
resistance  of  A'  equals  that  of  C.  If  B  be  ten  times  A,  X  is  ten 
times  C,  if  B  be  T  fg-  of  A,  X  is  T^T  of  <7,  etc. 

In  the  commercial  form  of  the  Wheatstone  bridge,  the  resist- 


ft 


1000  100 10 10 IOO     .     1000 

(^  <rc>  (^)  Q)  y  O~~  @> 


OJ200 


1 

?oo 


0 


^> 

C         0 

TT                             IT 

^ 

5 

1                 20 

/o 

20 

0 

0 

/OOO          2000 


T 


ances  ^4.  and  .5,  commonly  termed  the  "  ratio  arms  "  of  the 
bridge  and  the  variable  known  resistance  (7,  commonly  called 
the  "  rheostat  arm,"  are  geometrically  arranged  in  a  different 
manner  from  that  shown  in  Fig.  64,  in  order  to  economize 
space;  the  electrical  connections,  however,  remain  the  same. 

Post- Office  Pattern. 

The  arrangement  of  Wheatstone  bridge  coils  still  in  most  com- 
mon use  is  called  the  "  Post-office  pattern,"  it  being  the  form 


THE  MEASUREMENT   OF  RESISTANCE.  97 

adopted  by  the  British  Post-office  many  years  ago.  A  plan  view 
of  a  Post-office  bridge  is  given  in  Fig.  65,  the  wiring  connections 
being  shown  by  the  heavy  lines.  As  will  be  noted,  keys  are  in- 
serted in  the  battery  and  galvanometer  cir- 
cuits, in  order  that  these  may  be  manipulated 
at  the  will  of  the  operator.  The  separate  re- 
sistance coils  forming  the  bridge  and  rheostat 
arms  are  made  as  nearly  non-inductive  as  pos- 
sible, by  making  each  one  of  a  loop  of  wire, 
that  is,  a  wire  doubled  on  itself  before  wind- 
ing. After  being  adjusted  to  the  proper 
resistance  the  terminals  of  these  loops  are 
soldered  to  heavy  brass^  blocks,  as  is  shown 
in  Fig.  66.  Taper  plugs  may  be  inserted,  that  fit  snugly  be- 
tween the  members  of  each  pair,  which  when  in  place  short 
circuit  their  respective  coils  and  offer  a  negligible  resistance. 
To  insert  given  resistance  in  circuit,  therefore,  the  plug 
making  connections  between  the  two  terminals  is  simply  re- 
moved. 

It  is  common  to  give  the  resistance  coils  the  value  in  ohms 
indicated  by  the  numerals  in  Fig.  65.  As  can  be  seen  by  in- 
spection of  this  figure,  resistances  of  from  1  ohm  to  11,110 
ohms,  varying  by  steps  of  one  ohm  at  a  time,  are  attainable  in 
the  rheostat  arm,  by  pulling  out  the  proper  plugs,  and  the  ratio 
arms  may  be  adjusted  from  a  given  value  of  the  B  divided  by  A 
ratio,  of  100  to  1  to  a  value  of  same  ratio  of  T^,  thus  making 
the  theoretical  range  of  the  instrument  from  1,110,000  ohms 
to  .01  ohms. 

In  the  original  Post-office  pattern  bridge,  the  galvanometer,  the 
battery,  and  sometimes  even  the  galvanometer  and  battery  keys 
form  separate  pieces  of  apparatus.  These,  plus  the  bridge  itself 
and  the  necessary  connection  wires,  form  an  assemblage  of 
apparatus  that  is  too  bulky  and  awkward  to  use  for  ordinary 
commercial  work,  particularly  when  the  devices  have  to  be 
transported  from  place  to  place.  Combination  sets  in  which 
the  battery,  galvanometer,  and  keys  are  all  built  into  a  common 
carrying  case,  and  the  various  wiring  connections  between  them 
permanently  made,  are  the  favorites  to-day,  except  for  labora- 
tory work.  An  instrument  of  this  class  is  shown  in  Fig.  67. 
Here  the  battery  power  is  furnished  by  six  dry  cells  arranged  in 


98        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

a  separate  compartment  at  the  right,  and  cords  are  fitted  in  such 
a  way  that  any  number  of  the  cells,  from  one  up  to  six,  may  be 
used  at  will.  The  galvanometer  is  of  the  class  in  which  the 
moving  system  is  supported  by  pivots  instead  of  suspension 
fibers,  and  the  indications  given  by  a  needle  playing  over  a  scale, 
instead  of  a  beam  of  light,  as  in  the  reflecting  form.  This, 
while  not  as  sensitive  as  the  other  pattern,  is  sufficiently  so  to 
enable  readings  to  be  made  to  a  fraction  of  a  per  cent  when 
measuring  resistances  falling  within  the  favorable  range  of  the 
bridge  (.1  ohm  to  100,000  ohms).  It  is  compact,  does  not  require 
accurate  leveling,  and  is  sufficiently  robust  to  withstand  ship- 
ping. A  plug-reversing  switch  lettered  AXBll  in  the  figure  is 
inserted  in  the  bridge  arm  circuit.  By  means  of  this  the  con- 
nections of  the  bridge  arms  to  the  rest  of  the  network  may  be 


FIG.  67. 

reversed.  In  the  present  instance  this  extends  the  multiplying 
value  of  the  bridge  ratios  so  as  to  take  in  the  values  1,000, 
100, 10,  1,  .1,  .01,  and  .001. 

As  space  is  such  a  valuable  consideration  in  these  portable 
bridges,  provision  can  seldom  be  made  for  securing  specially 
high  insulation  of  the  terminals  and  key  contacts,  the  hard 
rubber  cover  on  which  all  are  mounted  being  supposed  to  give 
insulation  enough.  When  measuring  high  resistances  on  damp 
days,  however,  particularly  when  a  high  E.M.F.  from  some 
outside  set  of  batteries  is  being  used,  to  give  higher  sensibility, 
the  rubber  must  be  very  carefully  cleansed  and  dried  before 
making  readings,  as  otherwise  the  leakage  errors  may  become 
considerable. 


THE   MEASUREMENT  OF  RESISTANCE.  99 

Decade  Pattern. 

Wheatstone  bridges,  in  which  the  ratio  arms  and  rheostat 
values  are  altered  by  withdrawing  or  inserting  a  plug  for  each 
coil,  are  open  to  the  objection  that,  small  as  is  the  resistance 
of  each  individual  contact,  the  total  may  be  comparatively 
high,  particularly  after  the  plugs  become  slightly  tarnished,  and 
the  further  objection  that  the  continued  withdrawal  and  insertion 
of  a  plug  tends  to  loosen,  not  only  the  blocks  between  which  it 
wedges,  but  the  neighboring  ones  as  well,  thus  making  it  neces- 
sary to  go  over  a  whole  row  each  time  that  a  plug  is  moved,  to 
make  sure  that  the  others  have  not  been  affected.  There  is 
also  such 'a  large  number  of  plugs  that  it  becomes  a  very  easy 
matter  to  mislay  one  or  more  of  them  when  making  a  test. 

It  is  possible  to  overcome  these  drawbacks  to  a  considerable 


FIG.  68. 

extent  by  using  a  "  decade  "  type  of  bridge  in  which  the  rheostat 
arm  resistances  are  arranged,  as  shown  in  Fig.  68.  Here,  as  can 
be  seen,  a  resistance  is  cut  in  by  inserting  instead  of  withdraw- 
ing a  plug,  and  there  is  only  one  plug  with  its  corresponding 
contact,  to  each  unit,  ten,  hundred,  or  thousand  numeral  in  the 
total.  In  addition  to  this,  the  decade  arrangement  is  convenient 
because  it  is  formed  of  groups  of  coils,  in  which  each  member  of 
a  group  has  a  resistance  which  is  the  same  as  that  of  all  the 
other  members  of  the  group,  and  if  terminals  are  provided  so 
that  leads  may  be  attached  to  these  resistances,  the  various  coils 
may  be  intercompared  without  its  being  necessary  to  have  re- 
course to  outside  standards. 


100      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

The  plan  calls  for  a  greater  number  of  coils  than  the  "  Post- 
office  "  one,  with  a  consequent  higher  manufacturing  and  selling 
cost.  In  spite  of  this  it  is  now  rapidly  superseding  the  old 
arrangement,  as  the  greater  rapidity  of  working  and  the  higher 
accuracy  of  the  results  attained  more  than  offset  the  difference. 

A  portable  pattern  of  the  decade  type  of  set  is  shown  in  Fig. 
69,  Fig.  70  giving  the  wiring  connections. 

In  the  latter  the  block  marked  "  Galv."  is  so  connected  that 
when  a  plug  is  inserted  between  it  and  the  block  "  Int."  the  gal- 
vanometer indicated  in  the  figure  is  connected  into  the  bridge 
network,  and  used  in  obtaining  a  balance  in  the  regular  way. 


FIG.  G9. 


When  the  plug  is  transferred  to  the  gap  between  u  Galv."  and 
the  other  block,  the  gap  at  Gr  is  substituted  for  the  galvanometer 
in  the  set,  and  as  the  gap  has  binding-post  terminals,  an  outside 
high  sensibility  galvanometer  may  be  there  attached,  and  used 
for  more  accurate  work.  The  block  marked  "  Loop"  is  arranged 
so  that  when  a  plug  is  inserted  between  it  and  the  block  "  V&B," 
the  connections  of  the  set  are  such  as  to  form  a  regular 
Wheatstone  bridge,  the  unknown  resistance  to  be  measured 
being  inserted  at  X.  When  the  plug  is  changed  to  its  other 
position,  the  connections  become  those  for  making  the  "  Murray 
Loop  Test,"  for  the  location  of  faults,  as  described  on  page 


THE  MEASUREMENT  OF  RESISTANCE. 


101 


Any  number  of  the  five  cells  contained  in  the  box  may  be  uti- 
lized by  the  aid  of  the  connector  on  the  end  of  the  flexible  chord 
coming  up  through  the  rubber  top  between  the  ratio  arms,  or  that 
connector  may  be  left  free,  and  an  outside  source  of  E.M.F.  applied 
at  B,  whichever  the  user  may  desire.  The  keys  BK  and  GrK, 
for  the  battery  and  galvanometer  circuits  respectively,  are  su- 
perimposed, so  that  when  the  upper  one,  BK,  is  depressed,  first 
the  battery  and  then  the  galvanometer  circuits  are  completed, 
as  is  the  desirable  procedure  in  the  general  run  of  tests.  The 
end  of  the  key,  GrK,  is  extended  beyond  that  of  BK,  however, 
and  provided  with  a  separate  button,  so  that  if  desired  the 
galvanometer  circuit  may  first  be  closed.  As  this  set  measures 


FIG.  70. 

but  10  inches  by  6  inches  by  6|  inches,  it  evidently  forms  a 
convenient,  portable  device  for  covering  a  large  range  of 
measurements. 

Radial  Arm  Patterns. 

It  is  possible  to  dispense  entirely  with  plugs  in  bridges,  by 
using  sliding  contacts.  In  this  case  the  decade  system  of  coils  is 
usually  employed,  the  contacts  being  arranged  in  a  circle  over 
which  sweeps  the  end  of  a  contact  brush.  Such  bridges  are 
extremely  convenient  to  manipulate,  but  very  careful  design  and 
a  higher  grade  of  workmanship  than  for  a  plug  bridge  are  neces- 
sary, as  a  brush  sliding  over  a  flat  surface  cannot  cause  the  same 
intimate  contact  as  a  taper  plug  forced  into  a  hole  reamed  to 
receive  it  between  two  heavy  blocks,  and  variable  contact  re- 
sistances are  fatal  to  accuracy.  Crompton  &  Co.  make  "  dial 


102      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

switch  "  bridges,  as  they  call  this  type,  with  the  contacts  under 
plate  glass,  similar  to  the  scheme  used  by  the  same  concern  in 
their  potentiometer  shown  in  Fig.  56,  page  80.  The  brushes 
are  flat  and  rather  light,  and  are  turned  by  a  hard  rubber  knob 
coming  up  through  the  glass. 

In  the  Wolff  bridges,  one  of  which  is  shown  in  Fig.  71,  the 
contact  blocks  are  massive  pieces  of  brass,  and  the  brushes  that 
bear  on  them  are  formed  of  a  series  of  bronze  blades  fastened  to 
the  radial  arms  that  carry  them  at  an  angle  of  45  degrees.  In 
being  moved  from  one  position  to  another,  such  brushes  automat- 


FIG  71. 

ically  wipe  the  surfaces,  and  if  these  are  kept  slightly  moistened 
with  a  refined  light  mineral  oil,  as  directed,  they  will  be  found 
most  durable  and  extremely  satisfactory.  Tests  have  been  made 
on  such  bridges  which  showed  a  total  resistance  of  all  five  sets 
of  brush  contacts  in  series  of  less  than  .008  ohms. 

SLIDE-WIRE    BRIDGES. 

As  was  demonstrated  on  page  95,  it  is  not  necessary  that 
the  actual  values  of  the  resistances  of  the  coils  A  and  B  be 
known,  in  order  to  determine  X  in  terms  of  (7,  but  only  that 
their  ratio  be  known. 


THE   MEASUREMENT  OF  RESISTANCE. 


103 


If,  therefore,  we  select  a  fixed  value  of  C  and  vary  the  ratio 
of  A  to  B,  the  resistance  of  X  can  be  determined  by  application 

BC 

of  the  formula  X  =  — .     Devices  for  resistance  measurements 

yi. 

in  which  this  variable  ratio  arm  and  fixed  rheostat  arm  plan  are 
employed  are  geiierall  ycalled  "slide- wire  bridges"  and  are  con- 
structed as  follows  : 

In  Fig.  72  MN  is  a  wire  having  as  high  a  resistance  per 
unit  of  length  as  is  consistent  with  mechanical  strength,  and 
whose  ends  are  secured  to  heavy  brass  or  copper  bars.  A 
third  bar,  Q,  is  provided,  gaps  being  left  between  its  ends  and 
the  adjacent  terminals  just  named,  the  said  gaps  being  designed 
to  be  bridged  by  a  standard  resistance,  (7,  and  the  unknown  re- 


N. 


FIG.  72. 


sistance,  X,  to  be  measured  respectively.  Current  is  put 
through  this  network,  from  a  battery  whose  terminals  are 
attached  as  shown,  and  a  galvanometer,  6r,  is  likewise  provided, 
inserted  in  a  circuit  starting  from  the  point,  (J,  and  terminating 
in  the  sliding  contact,  $,  which  may  be  moved  along  the  wire, 
MN.  There  is,  further,  a  scale  beneath  MN,  that  is  uniformly 
divided  and  serves  to  measure  the  distance  between  the  contact 
and  the  points  of  attachment  of  the  bridge  wire.  It  will  be 
observed  that  the  arrangement  of  the  various  elements  is  exactly 
the  same  as  that  of  the  diagrammatic  Wheatstone  bridge  shown 
in  Fig.  64  and  as  like  parts  are  similarly  lettered,  the  relationship 


X  = 


BC1 


In  contradistinction   to    the    orthodox 


holds    good. 

Wheatstone  bridge,  however,  in  the  slide-wire  form,  the  rheo- 
stat arm,  (7,  is  constant  and  the  ratio  of  the  A  and  B  arms  to 


104      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

one  another  is  varied  until  a  balance  is  obtained,  this  being 
accomplished  by  sliding  S  along  MN. 

Fig.  72  is  simply  diagrammatic.  In  the  commercial  form  of 
slide-wire  bridge  there  are  at  least  two  other  air  gaps  in  0  and 
P  that  can  be  bridged  over  with  copper  straps  when  desired,  and 
there  is  also  a  wire  stretched  parallel  to  the  slide  wire  proper 
and  connected  to  one  terminal  of  the  galvanometer,  so  that  the 
sliding  contact,  &\  makes  connection  between  the  two,  and  the 
use  of  a  loose  wire  between  /S'and  the  galvanometer,  6r,  is  made 
unnecessary.  A  slide-wire  bridge  differing  in  these  particulars 
from  the  diagrammatic  figure  is  shown  in  Fig.  73. 

Accurate  results  are  seldom  obtained  from  a  single  reading 
with  the  simple  form  of  slide-wire  bridge  above  mentioned,  as 


--+<roiM&(Ajs*—— 
0 


r°n 


0 


©  @i 
© 


M  a  N 

FIG.  73. 

not  only  do  errors  arise  from  the  fact  that  the  exact  position  of 
the  contact  on  the  wire  may  be  erroneously  indicated  by  the 
index  attached  to  the  sliding  carriage,  but  the  resistance  of  the 
straps,  OP,  and  the  terminal  connections  incident  thereto,  all  of 
which,  by  hypothesis,  are  supposed  to  be  negligible  as  compared 
with  the  bridge  wire,  MN,  may  actually  be  a  considerable  factor. 
The  errors  due  to  these  causes  may  be  eliminated  by  making 
two  readings  in  determining  the  value  of  a  certain  resistance, 
first,  by  having  the  arrangement  as  shown  in  Fig.  72,  and  next, 
by  interchanging  the  O  and  X  coils.  Two  different  positions  of 
the  slide,  S,  on  the  wire  MN,  are  found  as  a  result,  and  from 
them  the  true  value  of  X  may  be  determined  from  the  follow- 
ing :  If  av  be  the  distance  from  M  to  8  at  the  first  reading 
and  #2  that  at  the  second  reading,  both  of  the  values  being 


THE  MEASUREMENT  OF  RESISTANCE.  105 

expressed  in  terms  of  the  units  of  length  into  which  the  bridge 
wire  is  divided  by  reference  to  its  accompanying  scale,  and  if  n 
be  the  total  number  of  units  of  bridge  wire  length,  we  have 

X  _  n  —  ^  +  g^ 
0        n  4-  ax  —  «2  ' 

In  this  equation  the  resistance  of  the  straps  does  not  enter  and 
the  error  due  to  observation  of  the  position  of  the  slider  is  also 
absent.* 

In  the  plain  form  of  bridge  the  length  of  the  bridge  wire, 
MN,  is  used  to  cover  the  whole  range  of  resistance  values  from 
zero  to  infinity,  namely,  when  S  is  at  JV,  and  B  is  therefore  zero, 
the  relationship 

v      BO  ,  00 

X  =  -    -  becomes    —  —  =  0, 
A  A 

and  when  8  is  at  M,  A  equals  zero,  whence 

BC     BO 

'"A"    "-Q- 

*  That  this  is  so  is  evident  from  the  following  derivation  of  the  formula 
(see  also  Stewart  and  Gee  Physics). 

Let  y  =  error  due  to  fact  that  point  of  contact  of  slide  on  wire  is  not  accu- 
rately shown  by  the  position  of  the  mark  on  the  slider  carriage 
relative  to  the  fixed  scale. 

r1  =  resistance  of  straps,  contacts,  etc.,  from  M  to  C. 
r2  =  resistance  of  straps,  contacts,  etc.,  from  N  to  X. 
n,a,  and  a2  having  values  as  before. 
Then  with  coils  as  in  Fig.  73 

B  =  n  -  (aj  +  y)  +  r2  and  A  =  at  +  y  +  rr 
^^B  ^n  -  a,-  y  +  r2 
C       A          a  +  y+r 


(2) 


when  coils  X  and  C  are  interchanged. 

A  =  a2  +  y  +  rt  and  B=  n  -  (a2  +  y)  +  r2, 
X  =  A  =      a,  +  y  +  r, 
C  ~B~n-a2-y+r2 

add  numerators  and  denominators  of  (1)  and  (2)  when 

X  _  n  4-  r2  +  r,  —  a,  +  «2 
C  =  n  +  r2  +  rt  +  al  -  a2 

r2  +  rl  can  be  stricken  out  of  both  numerator  and  denominator,  as  it  is  a 
small  quantity  added  to  a  relatively  very  large  one  in  both  cases,  whereupon, 

X  =  n-oL±«? 
C      n  +  at  -a2. 


106    ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

The  maximum  accuracy  of  reading  is  given  when  S  is  mid- 
way between  M  and  JV,  that  is  to  say  when  A  equals  B.  To 
increase  the  length  of  the  bridge  wire,  MN,  is  not,  as  a  rule, 
feasible,  for  if  it  be  made  in  excess  of  one  meter  the  apparatus 
becomes  entirely  too  bulky  and  difficult  both  to  read  and 
manipulate.  The  same  end,  however,  can  be  accomplished 
electrically  by  inserting,  as  is  shown  in  Fig.  74,  resistance  coils, 
5"  and  /.  These  in  effect  give  a  bridge  wire  whose  length,  as 
compared  with  that  of  the  slide  wire  alone,  is  the  ratio  between 
the  resistance  of  that  slide  wire  and  of  that  same  wire  plus  the 
coils  jffand  I.  For  example,  if  the  resistance  of  MN  were  10 
ohms,  and  in  order  to  obtain  the  maximum  sensibility  with  the 


34 


circuit  being  worked  on,  resistances  were  inserted  at  H  and  I 
each  having  a  resistance  of  495  ohms,  we  would  have  a  total 
resistance  in  the  ratio  arm  circuit  of  the  bridge  between  the 
points  of  attachment  of  the  battery  terminals  of  1,000  ohms  ; 
the  resistance  of  MN  is  thus  but  T^  of  the  resistance  of  the 
ratio  arms,  and  if  the  scale  beneath  this  wire  be  divided  into 
1,000  parts,  each  unit  step  of  the  contact,  S9  on  the  bridge  wire 
alters  the  ratio  of  the  length  of  B  to  A  by  one  one-hundredth 
part  of  a  thousand,  instead  of  one  part  in  a  thousand,  as  was  the 
case  before  the  resistances,  H  and  J,  were  inserted.  It  is  largely 
to  render  possible  the  insertion  of  such  resistances  that  the  ordi- 
nary slide-  wire  bridge  is  built,  as  illustrated  in  Fig.  73,  with  gaps 
between  N  and  X  and  O  and  M,  respectively.  In  Fig.  75  is 
illustrated  a  slide-  wire  bridge  which  has  not  only  gaps  for  the  in- 


THE  MEASUREMENT  OF  RESISTANCE.  107 

sertion  of  the  standard  and  unknown  resistances  and  for  the 
resistance  coils  for  electrically  lengthening  the  slide  wire,  but 
also  a  mechanical  arrangement  by  means  of  which  the  simple 
shifting  of  a  block  carrying  bent  copper  wires  reverses  the  con- 
nections of  X  and  C  and  so,  as  already  explained,  enables  the 
errors  due  to  failure  to  read  the  bridge  wire  contact  position 
correctly,  and  those  due  to  the  resistance  of  the  connecting 
straps  to  be  eliminated. 

Ohmmeters. 

A  commercial  form  of  the  slide-wire  bridge  is  the  so-called 
"ohrnmeter"  shown  in  Fig.  76.  Here  the  slide  wire  itself  is 
made  up  of  two  lengths,  one  of  them  starting  at  the  upper  post 
X  and  running  to  the  massive  square  bar  at  the  left,  and  the 
other  running  from  the  same  bar  back  to  the  lower  right-hand 


FIG.  75. 


binding-post.  The  square  bar  referred  to  is  supposed  to  be  of 
negligible  resistance  as  compared  with  the  wires,  so  that  the  latter 
may  be  considered  as  an  electrically  single  piece  which  has  been 
doubled  back  on  itself  merely  for  the  purpose  of  getting  it  into 
a  more  convenient  form.  The  source  of  current  is  a  set  of  dry 
cells  secured  inside  of  the  case,  and  a  tele  phone  receiver  is  used  as 
a  galvanometer,  it  having  the  advantages  for  that  purpose  men- 
tioned on  page  63.  The  battery  circuit  key  is  built  into  the 
telephone  receiver,  so  that  the  same  hand  that  holds  the  latter 
can  manipulate  the  battery  circuit.  The  stylus  shown  as  lying 
on  the  top  of  the  hard  rubber  bar  that  extends  lengthwise  of  the 
set  is  connected  in  the  receiver  circuit,  and  serves  both  as  the 
key  for  that  circuit  when  it  is  tapped  on  the  wire  and  as  an 
index  for  indicating  the  point  on  the  scale  where  balance  is  ob- 
tained. There  are  four  standard  resistance  coils,  usually  of  1, 


108     ELECTRIC  AND  MAGNETIC  MEASUREMENTS, 

10,  100,  and  1,000  ohms  value,  any  one  of  which  may  be  used  as 
the  "  C  "  arm  of  the  bridge  by  inserting  the  single  plug  shown 
in  an  appropriate  socket.  The  sockets  are  labeled  "  brown,  " 
"  blue,"  "  red,"  and  "  black,"  and  there  are  four  sets  of  numerals 
on  the  scale  printed  in  these  respective  colors,  the  purpose  being 
to  make  it  difficult  for  even  an  unskilled  observer  to  make  any 
mistakes  in  results,  as  when  the  plug  is  in  the  hole  labeled 
"  brown,"  the  brown  numerals  are  to  be  read,  when  in  the 
hole  labeled  "  blue,"  the  blue  numerals,  etc.  There  is  no 
necessity  of  making  any  computation  when  measuring  resist- 
ance with  this  bridge,  as  the  scales,  instead  of  being  equally 


FIG.  76. 

divided,  are  marked  off  directly  in  ohms.  That  this  is  possible 
is  evident  from  the  following:  Using  the  notation  of  Fig.  77, 
which  shows  diagrammatically  the  connections  of  the  ohmmeter, 
it  is  clear  from  the  law  of  the  Wheatstone  bridge  that 

A:  Si:  C'.X. 

Now  A  +  B  is  the  total  length  of  the  doubled-up  wire,  which 
in  the  actual  instrument  is  30",  hence,  B—  30"  —  A.  C,  the 
standard  coil,  has  a  resistance  of  say  1  ohm.  The  formula 
then  becomes, 

A  ~\  ^0"          A 

-*i.  ._.  _-         tj\j     —  _/j_ 

n  /\  *  •  ~i       -TT-  7  Ol  -/A.      5 


or  in  other  words,  for  each  value  of  JT,  there  is  a  single  corre- 
sponding value  of  .4,  which  may  thus  be  marked  on  the  scale. 


THE  MEASUREMENT  OF  RESISTANCE. 


109 


If  Q  be  made  10  ohms,  the  value  of  X  is  evidently  multiplied 
by  ten  also,  that  is  to  say,  the  values  of  the  scale  readings  are 
multiplied  by  ten.  The  same,  of  course,  applies  to  other  values 
of  the  C  coil. 

THE    VARLEY    BRIDGE. 

It  can  be  shown  that  in  measuring  high  resistances  with 
a  Wheatstone  bridge  or  with  a  slide-wire  bridge  it  is  de- 
sirable to  have  the  resistance  of  the  A  and  B  bridge  arms 
(see  Fig.  64 ),  or  of  the  slide  wire  as  a  whole,  high  also. 
This  is  not  feasible  with  the  ordinary  slide-wire  bridge  or  the 
ohmmeter  just  described ;  for  if,  using  suitable  commercial 
alloys,  a  total  resistance  of  about  15  ohms  for  the  slide  wire 


-vuM&iu^=- 


FIG.  77. 

be  exceeded,  the  diameter  of  the  wire  becomes  too  small 
to  be  strong  mechanically,  or  to  withstand  the  wear  of  the 
contact  devices  without  introducing  appreciable  errors  due  to 
the  destruction  of  the  uniformity  of  the  resistance  of  the  wire 
throughout  its  length.  The  simple  expedient  of  increasing  the 
geometrical  length  of  the  wire  cannot  be  far  extended,  because, 
as  already  explained,  this  makes  the  apparatus  too  bulky.  It 
is,  however,  possible  to  lengthen  the  wire  electrically  without 
spreading  it  over  a  greater  length,  this  being  accomplished  by 
forming  it  of  a  set  of  coils  of  wire  of  like  resistance,  all  con- 
nected in  series  and  each  provided  with  terminal  buttons  with 


110      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

which  the  device  corresponding  to  the  slide-wire  contact  makes 
connection.  An  arrangement  of  this  simple  kind  is  shown  in 
Fig.  78,  in  which  if  each  of  the  10  coils  have  a  resistance  of 
1,000  ohms  Ave  have  the  exact  equivalent  electrically  of  a  slide 
wire  having  a  resistance  of  10,000  ohms,  but  contact  with  it 
can  be  made  only  at  ten  equidistant  points.  *  Ten  steps  in  the 
bridge-wire  resistances  evidently  fail  to  provide  means  for 
making  close  adjustment ;  in  fact,  it  should  be  possible  to  have 
1,000  steps  to  equal  the  plain  slide-wire  bridge,  the  position 
of  whose  contact  can  almost  invariably  be  read  to  that  fraction 
of  its  length.  It  is,  of  course,  out  of  the  question,  on  the  score 
of  price  and  bulk,  to  make  the  apparatus  contain  1,000  coils 
each  of  1,000  ohms  resistance,  but  the  same  end  may  be  accom- 
plished by  using  the  electrical  vernier  described  in  connection 


@i 


m. 


G 


N 


FIG.  78. 


with  the  potentiometer  on  page  82,  which  plan  for  the  poten- 
tiometer was  copied  from  the  bridge,  as  devised  by  Varley. 
The  elementary  Varley  bridge  is  diagrammatically  shown  in  Fig. 
79,  and  consists  of  a  series  of  11  coils  each  of  1,000  ohms 
resistance,  and  of  10  coils  each  of  20  ohms  resistance,  con- 
nected in  series,  and  with  the  terminals  of  the  latter  series  held 
with  a  fixed  distance  between  them  by  a  carriage  movable  along 
the  contact  buttons  attached  to  the  1,000  ohm  coils.  From  the 
potentiometer  description  it  can  readily  be  seen  that,  using  the 
two  terminals  attached  to  the  20  ohm  coils  and  the  galva- 
nometer terminal  sliding  on  the  contact  buttons  of  the  20  ohm 
coils,  the  device  is  capable  of  inserting  in  the  galvanometer 
circuit  between  the  point  M  and  the  connection  running  to  the 
galvanometer,  resistances  between  zero  and  10,000  ohms,  in 


THE    MEASUREMENT  OF   RESISTANCE. 


Ill 


steps  of  10  ohms  each,  or  in  other  words,  by  steps  of  one  one- 
hundredth  at  a  time. 

As  at  least  1,000  steps  are  needed  for  accurate  work,  the  com- 
mercial form  of  Varley  bridge,  commonly  termed  the  "  Thompson 
Varley  slide,"  is  built  with  101  coils  of  1,000  ohms  each,  and  100 
vernier  coils  of  20  ohms  each.  The  coils  are  in  separate  boxes 
with  the  contact  buttons  arranged  in  circles,  as  shown  by  the 
illustration  of  the  device,  Fig.  80,  and  the  contact  arms  are 
pivoted  in  the  center  of  these  circles.  Connections  are  made 
as  in  Fig.  81.  Readings  can  be  taken  to  one  part  in  ten  thou- 
sand, there  being  that  many  steps  available,  namely,  one 


FIG  79. 

hundred  variations  on  each  of  the  one  hundred  positions  of  the 
double  arm. 

The  high  resistance  of  the  coils  entering  into  the  construc- 
tion of  this  Varley  slide  make  the  accuracy  very  high,  but  the 
number  of  the  coils  is,  on  the  other  hand,  high  also,  and  the 
resultant  cost  prohibits  its  use  in  many  cases. 

The  electric  vernier  principle  may  be  employed  to  make  a 
cheaper  slide  with  fewer  coils  but  the  same  number  of  steps  by 
simply  extending  it  further,  putting  a  slide  on  a  slide.  Each 
added  group  of  ten  slide  coils  multiplies  the  possible  number  of 
steps  by  ten,  but  on  the  other  hand  adds  one  more  to  the 
number  of  contact  arms  that  must  be  adjusted  to  get  the 
balance. 


112       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

An  instrument  in  which  this  slide  on  slide  plan  has  been 
carried  to  an  extreme  is  the  Cushman  bridge,  where  there  are 
five  sets  of  coils,  which,  theoretically,  would  enable  the  com- 
parison of  two  nearly  equal  resistances  to  an  accuracy  of  .0002 
per  cent.  In  practise,  however,  such  refinement  is  as  absurd 
as  the  array  of  figures  after  a  decimal  point  that  is  often 
indulged  in  in  figuring  the  horse-power  of  an  engine,  from 
indicator  cards,  as  the  errors  due  to  slight  differences  in  coil 
resistances,  to  the  contacts,  to  temperature,  etc.,  amount  to 
many  times  this  percentage. 

VOLT    AND   AMMETER   METHODS. 

From  Ohm's  law  it  is  clear  that  if  the  current  passing  through 
a  resistance  be  measured  and  the  difference  of  potential  between 


the  terminals  of  the  resistance  simultaneously  noted,  the  value 
of  the  resistance  can  at  once  be  figured,  by  dividing  the  value 
of  the  latter  observation  by  the  former.  This  method  of  resist- 
ance measurement  is  one  of  somewhat  limited  application  as 
regards  the  range  of  resistance  that  it  can  cover ;  for,  where  the 
resistance  is  high,  the  current  through  it  must  usually  be  kept 


THE  MEASUREMENT  OF  RESISTANCE. 


113 


of  a  very  low  amperage  in  order  to  avoid  heating  errors  or  actual 
burning  out,  and  instruments  for  the  measurement  of  very  low 
amperage,  having  but  limited  application,  are  but  seldom  on 
hand  ;  if,  on  the  other  hand,  the  resistance  be  low,  the  current 
required  to  cause  a  closely  measurable  drop  becomes  corre- 
spondingly high,  and  it  is  not  always  convenient  to  procure  a 
source  of  such  heavy  current,  or  an  instrument  for  measuring  it. 
It  should  be  noted  that  unless  the  potential-measuring  instru- 
ment is  one  that  consumes  no  current,  namely,  is  of  practically 
infinite  resistance,  as  in  the  case  of  the  electrostatic  device, 
errors  are  introduced.  Referring  to  Fig.  82,  if  IT  be  the  resist- 
ance, A  the  current  measuring  instrument,  V  the  potential 
measuring  instrument,  and  B  the  source  of  current ;  while  the 
meter,  F,  indicates  the  true  potential  difference  at  the  terminals 


FIG.  81. 


of  IF,  if  it  be  in  calibration ;  A  gives,  not  the  current  through 
IF  alone,  but  through  the  circuit  formed  by  IF  as  shunted  by 
the  resistance  of  the  instrument,  V.  If  the  only  other  possible 
scheme  of  connection  be  used,  as  shown,  in  Fig.  83,  the  state  of 
affairs  is  reversed,  for  while  A  now  shows  only  the  current 
flowing  through  W,  V  indicates  the  drop  due  to  the  flow  of 
that  current,  not  only  through  that  resistance,  but  also  that  of 
the  instrument  A. 

That  these  errors  are  by  no  means  inconsiderable  will  be  evi- 
dent from  the  following  examples  :  Take  first  the  connections 
shown  in  Fig.  82.  Let  the  range  of  the  voltmeter,  V,  be  1  volt 
and  its  resistance  100  ohms,  the  range  of  the  ammeter  A  be  1 
ampere  and  its  resistance  .05  ohms,  and  the  true  value  of  the 
resistance  IF  be  1  ohm. 


114       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

Adjust  the  current  from  the  battery  B  by  a  rheostat,  or  other 
convenient  means,  until  the  ammeter  shows  exactly  1  ampere. 
The  voltmeter  V  will  then  show,  not  1  volt,  as  would  be 
necessary  in  order  that  the  solution  of  Ohm's  equation  should 
give  a  value  of  W  of  1  ohm,  but  .99  volt,  because  the  resist- 
ance of  the  circuit  formed  by  the  resistance  W  shunted  by  the 

voltmeter  is,  from  the  law  of    divided  circuits,       =  =  .99 

ohms  (nearly)  and  the  drop  in  potential  across  the  terminals  with 
one  ampere  flowing  would  be  .99  volts.  Neglect  to  take  into 
consideration  the  finite  value  of  the  resistance  of  the  voltmeter 
would  therefore  cause  an  error  of  1  per  cent  in  the  calcu- 
lated result.  Take  now  the  connections,  as  in  Fig.  83,  the  other 
conditions  remaining  as  before.  The  voltmeter  V  would  now 


W 


FIG.  82. 

show  1.05  volts,  as  this  is  the  drop  across  the  terminals  of  a 
circuit  of  1.05  ohms  resistance  with  1  ampere  flowing,  and  the 
calculated  value  of  W  would  hence  be  1.05  ohms  instead  of  its 
true  value  of  1  ohm,  which  is  an  error  of  5  per  cent.  It 
will  thus  be  seen  that,  unless  the  measurements  are  to  be  of  the 
roughest,  due  allowance  must  always  be  made  for  the  resistance 
of  the  instruments. 

MEASUREMENT  OF  Low  RESISTANCES. 

The.  Wheatstone  and  slide-wire  bridges  are  not  suitable  for 
measuring  low  resistances,  that  is  to  say,  those  having  a  value 
of  .1  ohm  or  under,  as  the  resistance  that  these  devices  measure 
is  the  total  resistance  between  the  junction  of  the  B  and  C  arms 


THE   MEASUREMENT   OF   RESISTANCE.  115 

(see  Fig.  64)  with  X,  and  include,  not  only  X  itself,  but  the 
leads  used  to  make  connection  between  X  and  the  bridge,  and 
of  all  of  the  contacts  in  that  circuit.  The  resistance  of  the 
leads  is  nearly  constant,  but  their  value  may  be  so  large,  as  com- 
pared with  that  of  the  resistance  under  test,  that  a  very  small 
error  in  the  measurement  of  the  total  would  be  an  exceedingly 
large  percentage  of  the  value  of  the  unknown  resistance,  and 
hence  the  test  entirely  unsatisfactory. 

The  resistances  of  the  contacts  are  not  even  constant,  as  these 
depend  on  the  pressure  between  them,  the  condition  of  the  sur- 
faces, and  their  area.  They  may  easily  vary  some  thousandths 
of  an  ohm  in  value,  even  under  favorable  circumstances,  and 
with  a  value  of  IT  as  high  as  .1  ohm,  each  thousandth  would  rep- 
resent 1  per  cent. 

It  is  evident,  therefore,  that  for  the  measurement  of  low  resist- 


A  W 


B 


FIG.  83. 

ances  methods  should  be  employed  in  which  the  resistance  of 
the  leads  and  contacts  does  not  enter  into  the  results. 

KIRCHHOFF    BRIDGE. 

The  earliest  device  of  this  type  seems  to  have  been  the 
Kirchhoff  bridge,  a  device  that  was  probably  due  to  Heaviside, 
who  described  it  in  the  early  seventies.  The  instrument  used 
in  this  method  is  a  differential  galvanometer  ("Galv.,"  Fig.  84) 
and  the  low  resistance  X  to  be  measured  is  connected  in  series 
with  the  standard  resistance,  S,  the  current  flowing  through 
both  being  taken  from  a  source,  B,  capable  of  supplying  con- 
siderable current.  The  resistance  of  the  standard,  S,  between 
two  points,  A  and  (7,  must  be  accurately  known,  and  the  bar  of 


116        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

metal  forming  it  must  be  divided  between  these  points  into  as 
many  equal  resistance  steps  (often  one  hundred)  as  possible,  by 
appropriate  markings.  Contacts  M  and  N  make  contact  with 
the  standard  bar  S,  and  the  similar  contacts  P  and  Q  make 
connection  at  the  ends  of  the  unknown  bar. 

The  electrical  connections  are  so  made  by  the  contacts  that 
the  current  through  the  coil  of  the  differential  galvanometer  due 
to  the  difference  of  potential  between  the  points  M  and  N 
tends  to  cause  a  deflection  opposite  to  that  which  would  be 
given  by  the  current  through  the  other  coil,  due  to  the  differ- 
ence of  potential  between  Q  and  P.  N,  Q,  and  P  being  fixed, 
M  is  moved  along  S  until  the  galvanometer  shows  no  deflec- 
tion. The  resistance  of  the  bar,  X,  between  the  points  Q  and 


r 

Q 

~7   C>;/\>O  T" 

o.()o. 

-W- 

1 

V 

[I||l[!lli|lll!|llll[llN|llll|llll[lll!|!lll|llll[!ll!|!i!l|llll]!lllJllll}lllljllll|lll|i 

N                          p 

_J  :  L_J 

FIG.  84. 


P  is  then,  from  Ohm's  law,  the  resistance  of  that  part  of  the 
bar,  $,  included  between  M  and  7V,  for  the  same  current  flows 
through  both,  as  they  are  connected  in  series,  and  the  drops  in 
potential  are  alike,  as  the  galvanometer  shows  no  deflection. 
The  resistance  of  the  battery  leads,  of  the  wire  joining  the  two 
resistances  and  at  the  points  of  contact  of  these  with  the  bars, 
do  not  enter,  as  they  are  not  in  the  measuring  circuit  and  merely 
affect  the  current  strength.  The  resistance  between  the  con- 
tacts, Af,  TV,  (?,  and  P,  and  their  resistance  bars,  do  not  enter 
either,  as  they  are  negligible  in  comparison  with  the  high  resist- . 
ance  of  the  galvanometer. 

As  the  accuracy  of  results  obtained  by  this  method  depends 
on  having  a  galvanometer  that  is  truly  differential,  the  instru- 


THE    MEASUREMENT    OF   RESISTANCE. 


117 


ment  should  be  tested  for  that  quality  before  use.  To  do  so, 
connect  the  two  coils  in  series,  but  in  opposition,  and  pass  a  very 
weak  current  through  them,  whereupon  there  should  be  no  deflec- 
tion. The  coils  should  then  be  coupled  in  opposition  but  in 
parallel,  and  current  again  applied;  if  there  is  still  no  deflection, 
the  coil  resistances  are  alike.  The  latter  test  is  the  one  actually 
determining  the  fitness  of  the  apparatus  for  use  in  making  this 
test,  as  while  if  it  shows  no  deflection  the  instrument  may  still 
not  be  truly  differential,  any  error  due  to  that  cause  is  offset 
by  a  difference  in  coil  resistances. 

The  galvanometer  should  also  be  tested  to  see  that  its  two 


~v * 


FIG.  85: 


coils  are  insulated  from  one  another  so  that  no  current  can  flow 
between  them. 

MEASUREMENTS    WITH   AN    AMMETER. 

Low  resistances  of  nearly  the  same  value  can  be  measured 
with  the  aid  of  commercial  ammeters  of  the  type  in  which  the 
shunts  are  separate  from  the  instruments  themselves,  provided 
that  the  resistance  of  their  shunts  is  known.  For  instance, 
referring  to  Fig.  85,  A  represents  the  ammeter,  S  its  shunt,  X 
the  unknown  resistance,  and  B  the  source  of  current.  The 
same  current  flows  through  $  and  X,  as  they  are  connected  in 
series ;  and  if  the  ammeter  A  be  one  in  which  the  angular  deflec- 


118       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

tions  of  the  needle  are  proportional  to  the  current  strengths,  or 
even  if  this  be  not  so  and  the  scale  be  divided  so  as  to  indicate 
current  strength,  X  may  be  found  in  terms  of  S,  from  the  fact 
that,  as  will  be  evident  on  consideration,  the  drop  across  S  is 
to  the  drop  across  X  as  the  resistance  of  S  is  to  the  resistance 
of  X.  For  instance,  if  the  current  through  S  gives  a  deflection 
of  ten  scale  divisions  on  the  instrument,  A,  and  that  across  X, 
when  the  terminals  of  the  instrument  are  shifted  to  take  up  the 
position  shown  by  the  dotted  lines  be  twenty  scale  divi- 
sions, then  X  is  twenty  tenths,  or  two  times  8.  A  few 
manufacturers  make  the  drop  of  all  of  their  shunts  uni- 
form, for  instance,  50  millivolts  when  worked  at  maximum 
load.  From  this  data  the  resistance  of  the  shunt  between 
the  points  at  which  the  connection  to  the  instrument  is 


U^CX^^N 

T                                          T' 

c 

c 

H  ^|ii"|""|""|"'1'i"|""h'l'"'|i4't"'l'H'H""l""l'"'l'Hl"t4  I [ K 

f      •  I 

v ±^z^^*r f 

FIG.  86. 

made  is  easily  figured;  that  of  a  100  amperes  hunt  on 
the  50  millivolt  basis  being  .005  ohms,  and  that  of  a  1,000 
ampere  shunt  .0005  ohms,  etc.  If  in  this  example  the  current 
strength  supplied  by  B  be  such  that  the  instrument,  A,  gives 
a  reading  of  ten  scale  divisions  when  its  terminals  are  at- 
tached to  a  shunt  of  100  amperes  capacity,  S,  a  resistance,  X, 
in  series  with  S,  the  drop  across  which  causes  one  scale  divi- 
sion deflection,  will  have  a  value  of  .0005  ohms,  or  generally,  if 
the  resistance,  X,  give  JV  scale  divisions  deflection,  it  has  a  value 
of  .0005  N"  ohms.  The  resistance  of  A  is  usually  sufficiently 
high  so  that  the  resistance  of  the  contacts  between  its  leads 
and  the  S  and  X  resistances  is  negligible,  and  such  work  as 
measuring  the  resistance  of  armature  coils  can  therefore  be 
rapidly  and  accurately  conducted  with  inexpensive  apparatus. 


THE   MEASUREMENT  OF    RESISTANCE.  119 

THE   THOMSON    DOUBLE   BRIDGE. 

The  Kirchhoff  bridge  necessitates  the  use  of-  a  differential 
galvanometer,  and  this  instrument  is  not  often  available.  Lord 
Kelvin  devised  a  modification  of  this  bridge,  which  renders  it 
possible  to  use  an  ordinary  galvanometer,  the  connections  being 
as  shown  in  Fig.  86.  The  leads  from  the  standard  and  un- 
known resistances  are,  as  is  seen  from  the  figure,  connected,  so 
that  the  E.M.F.'s  at  their  terminals  are  opposed,  and  when  these 
are  equal  the  galvanometer  of  course  gives  no  deflection.  The 
standard  bar  >S  is  divided  up,  so  that  fractions  of  its  length,  and 
hence  resistance,  may  be  read  off,  as  in  the  Kirchhoff  bridge ; 
and  when  the  sliding  contact,  (7,  which  is  adjustable  along  its 
length,  reaches  the  point  where  the  galvanometer  gives  no  de- 

A  C 

1000    100    10  10     IOO 


'  -  /""^-»--o<a'^U«-v 


-V~0{£&/IA*+ 

FIG.  87. 

flection,  the  resistance  between  the  fixed  terminal  and  the 
movable  one  is  evidently  that  between  the  terminals,  T  and  2*', 
of  the  resistance  to  be  measured.  In  the  actual  Kelvin,  or  as 
it  is  still  more  generally  known,  the  Thomson  double  bridge, 
there  are  inserted  in  the  leads  between  the  galvanometer  and 
the  standard  and  unknown  resistances,  resistance  boxes,  the 
value  of  whose  resistance  may  be  varied  by  withdrawing  the 
plugs,  as  is  shown  in  Fig.  87.  If  the  resistance  of  P  be  made 
equal  to  R,  and  that  of  A  to  (7,  the  resistance  of  the  unknown 
bar,  X,  is  read  off  directly  from  the  standard  bar,  as  above  out- 
lined. If,  however,  the  ratio  of  R  to  P  be  made,  for  instance, 
ten,  and  that  of  O  to  A  ten,  the  resistance  of  X  is  ten  times 


120       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

that  of  S,  and  vice  versa  when  the  ratios  are  interchanged,  just 
as  in  the  case  of  the  ratio  arm  coils  in  the  Wheatstone  bridge. 

A  commercial  form  of  the  Thomson  double  bridge  suitable 
for  measuring  resistances  ranging  from  1  ohm  down  to  .000001 
ohm  (1  micro-ohm),  and  termed  a  "  micro-ohmmeter,"  is  illus- 
trated in  Fig.  88,  the  connections  being  as  shown  in  Fig.  89. 
In  this  instrument  the  standard  resistance  is  a  calibrated  plati- 
num silver  alloy  bar  having  a  resistance  of  .01  ohm  between 
the  points  designated  by  zero  and  100  on  the  scale  placed 
parallel  to  it.  With  the  aid  of  suitable  terminals,  the  unknown 
resistance  is  placed  in  series  with  this  and  a  battery,  and  a 
movable  contact,  M,  is  slid  along  the  standard  until  the  galva- 


FIG.  88. 

nometer,  which  is  built  into  and  forms  part  of  the  apparatus,  no 
longer  shows  a  deflection.  If  the  resistances  of  the  ratio  arm 
coils  then  have  a  ratio  of  unity,  the  resistance  of  the  unknown 
bar  is  read  off  directly.  Varying  ratios  of  the  resistance  of  the 
ratio  arm  coils  are  obtained  by  sliding  the  carriage  C  along  its 
guides,  in  this  way  giving 'the  apparatus  a  range  of  from  one 
hundred  times  that  of  the  maximum  resistance  of  the  standard 
bar,  that  is  to  say  1  ohm,  to  one  one-hundredth  of  the  mini- 
mum resistance  readable  on  the  standard  bar,  that  is  to  say  1 
micro-ohm.  The  numerals  2,  3,  4,  5,  and  6,  that  are  displayed 
through  the  opening  in  the  carriage  C  when  resting  on  different 
contacts,  show  the  number  of  decimal  points  to  be  stepped  off  in 


THE  MEASUREMENT  OF  RESISTANCE. 


121 


noting  down  the  readings.  If,  for  instance,  the  galvanometer  be 
brought  to  a  position  of  zero  deflection  when  the  movable  con- 
tact, M,  stands  at  the  scale  division  numbered  44,  the  resistance 
of  X  is  .44  ohms,  if  the  numeral  2,  indicating  two  decimal 
places  to  be  stepped  off,  be  visible  through  the  opening  in  C. 
If  the  numeral  5  were  visible  through  the  said  opening  at  the 
time,  five  decimal  points  would  have  to  be  stepped  off,  and  the 
resistance  of  X  would  be  .00044  ohm.  A  strap,  6r,  connecting 
two  binding  posts  at  the  top  of  the  instrument,  is  provided,  and 
when  it  is  removed  a  sensitive  reflecting  galvanometer  may  be 
inserted  when  it  is  desired  to  make  determinations  of  a  high 
degree  of  accuracy. 

As  in  all  Thomson  double  bridge  measurements,  this  appara- 
tus gives  results  that  are  independent  of  the  resistance  of  the 


hln-1'.nli.i.li.nln.il..nln.il.ul.nl.inlH..l.i..h®    m.|l.l.|i.H|.iil|nil|iinlH-»'|"N|""|Nu|nH|in.|HM|.,n|l,n|,,i1^ 


FIG.  89. 


J 


leads  running  from  the  unknown  bar  to  the  instrument  and  of 
the  contacts  between  it  and  the  lead  terminals,  for  these  are  neg- 
ligible in  comparison  with  the  resistance  of  the  galvanometer 
and  the  ratio  arm  coils.  As  the  method  is  a  zero  one,  in  which 
determinations  are  made  when  no  current  is  flowing  through 
the  galvanometer,  it  is  independent  of  variation  in  the  sensibil- 
ity of  this  also.  The  complete  apparatus  is  inclosed  in  a  small, 
light  carrying-case,  and  the  storage  battery  that  is  sometimes 
supplied  with  the  equipment  is  likewise  compact  and  light,  so 
that  we  have  a  truly  portable  device  for  the  measurement  of 
very  low  resistances.  The  method  of  operation  is  so  simple 
that  reliable  results  may  be  obtained  when  placed  in  the  hands 
of  an  unskilled  workman. 


122       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 
THE   CAREY-FOSTER   METHOD. 

The  slide -wire  bridge  may  be  used  to  determine  with  a  high 
degree  of  accuracy  the  difference  in  resistance  between  two  coils 
of  nearly  equal  value.  To  accomplish  this  a  balance  is  first 
obtained  with  the  standard  and  unknown  coils  connected  in  the 
bridge  circuit,  as  shown  at  8  and  X,  Fig.  90,  respectively,  and 
then  the  second  determination  is  made  with  8  and  X  interchanged. 
The  bridge  wire  reading  in  the  latter  case  will  be  different  from 
that  in  the  former,  and  the  resistance  of  the  bridge  wire  in- 
cluded between  the  points  where  contact  was  made  when  the 
balances  were  attained  is  the  difference  in  resistance  between  S 
and  X .  This,  of  course,  makes  it  necessary  that  the  resistance 
per  unit  of  length  of  the  bridge  wire  be  known,  and  this  is  some- 
thing that  can  be  determined  in  several  ways.  If,  for  instance, 


FIG.  90. 

we  have  two  coils,  whose  resistances  differ  by  a  known  amount, 
the  resistance  per  unit  length  of  slide  wire  can  be  obtained 
directly  from  the  above  relationship,  the  unknown  value  then 
being  that  of  the  bridge  wire,  whereas  the  !S  and  X  in  the 
formula  are  known.  Another  method  is  similar  to  that  used  in 
determining  the  uniformity  of  the  drop  along  a  potentiometer 
wire,  as  mentioned  on  p.  76.  Even  if  we  have  but  a  single 
standard  resistance,  having  a  value  of  say  1  ohm,  we  can  make 
up  an  exact  duplicate  of  it  of  any  resistance  wire,  and  then 
shunt  one  of  the  two  by  a  known  resistance  of  considerably 
higher  value,  say  100  ohms.  The  ratio  of  the  shunted  resistance 

to  the  unshunted  standard  one  is  now ='  .9901  to  one, 

which  gives  us  a  means  of  calibrating  the  bridge  wire  in  steps 
of  .0099  ohm  each. 


THE    MEASUREMENT   OF   RESISTANCE. 


123 


As  the  bridge  wire  may  be  made  of  a  large  diameter  to 
advantage,  a  long  length  represents  only  a  small  resistance,  so 
that  two  resistances  of  nearly  equal  value  may  be  compared  very 
accurately.  This  method  is  so  delicate  that  it  becomes  probably 
the  most  valuable  one  for  use  in  determining  the  temperature  co- 
efficient of  metals,  the  one  portion  of  the  specimen  being  main- 
tained at  a  uniform  normal  value  by  immersion  in  an  oil  bath,  and 
that  of  the  section  from  which  the  temperature  coefficient  is  to 
be  determined  immersed  in  a  similar  bath  whose  temperature  can 
be  varied  as  desired.  If  the  two  sections  be  first  adjusted  to  have 


FIG.  91. 


the  same  resistance  at  the  same  temperature,  and  one  be  then 
raised  to  some  new  temperature,  the  resistance  of  the  wire 
between  the  balancing  points  on  the  bridge  wire  is  the  increase 
in  resistance  due  to  that  temperature  change.  By  making  a 
series  of  determinations  in  this  way,  the  curve  showing  the 
relation  between  the  temperature  and  resistance  of  any  given 
specimen  of  conductor  may  be  drawn. 

Since,  in  order  that  the  temperature  may  be  properly  controlled 
and  accurately  measured,  it  is  necessary  that  each  specimen  be 
immersed  in  a  bath  of  oil,  which  is  constantly  stirred,  it  is 


124       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

advantageous  to  provide  some  means  of  interchanging  the  coils 
electrically  instead  of  mechanically,  in  order  to  avoid  moving 
them  about  by  hand.  The  regular  slide-wire  bridge  can  be 
made  to  answer  these  requirements  if  the  connections  thereon 
be  arranged  as  shown  in  Fig.  91,  the  double  circles  in  this 
figure  indicating  mercury  cups.  The  apparatus  for  electrically 
interchanging  the  position  of  the  coils  consists  of  a  pair  of  hard 
rubber  squares  drilled  near  the  corners  to  receive  U-shaped 
pieces  of  heavy  copper  wire  carefully  amalgamated  at  their 
ends  and  supported  only  loosely  by  the  framework,  so  that 
their  weight  acting  downward  makes  a  good  contact  between 
their  lower  faces  and  the  bottom  of  the  mercury  cups  in  the 
bridge.  When  this  apparatus  is  placed  so  that  the  copper  con- 

,S 


S' 


FIG.  92. 

nectors  ad,  he,  ik,  and  jl  have  the  positions  shown  in  the  figure, 
the  connection  of  the  standard  coil  is  in  the  gap  in  the  bridge 
opposite  to  that  which  it  occupies  when  the  blocks  have  been 
lifted  and  rotated  90  degrees  about  a  vertical  axis. 

For  slide-wire  bridges  not  supplied  with  connections  and 
terminals  for  the  use  of  the  reversing  commutator  just  described, 
a  separate  commutator  is  often  used,  one  of  these  being  shown 
in  Fig.  92. 

A  compact  Carey-Foster  bridge  and  commutator  combined  is 
shown  in  Fig.  93,  the  plan  view  being  given  above  the  perspec- 
tive one.  The  bridge  wire  is  very  short  in  this  piece  of 
apparatus,  and  protected  from  radiation  by  a  hard  rubber  strip,  so 


THE  MEASUREMENT  OF  RESISTANCE. 


125 


that  there  is  little  probability  of  error  due  to  thermal  E.M.F's. 
By  means  of  shunts,  one  of  which  is  shown  detached  and  placed 
alongside  of  the  apparatus,  the  value  of  the  bridge  wire  may  be 
varied  as  desired.  The  commutating  device  is  double,  and  when 
manipulated  by  raising  and  turning  the  upper  knurled  hard  rub- 
ber button  exchanges  the  resistance  coils  and  battery  connections 
simultaneously  ;  whereas  when  the  lower  button  alone  is  raised 
and  given  a  quarter  of  a  revolution,  the  battery  connections 
alone  are  reversed. 

CONDUCTIVITY    BRIDGES. 

For  the  rapid  commercial  measurement  and  comparison  of  low 
resistances,    such    as  the  measurement   of  the  conductivity  of 


FIG.  93. 


samples  of  large  copper  wires,  a  modified  form  of  Carey-Foster 
bridge,  known  as  the  conductivity  bridge,  is  often  employed. 
The  diagram  of  the  connections  in  this  device  is  given  in  Fig. 
94,  a  perspective  view  of  the  complete  apparatus  being  given  in 
Fig.  95. 

The  method  of  operation  is  as  follows :  In  the  figure  C  0'  is 
the  bar  under  test,  the  same  being  secured  in  place  by  the  heavy 
clamps  shown  ;  A  and  A'  are  ratio  coils  of  equal  value,  usually 
wound  together  so  that  they  will  always  be  at  the  same  tempera- 
ture ;  and  Sl  and  /$,  are  two  resistances  made  of  material  having 
the  same  temperature  coefficient  as  the  specimen  under  test ;  R 


126       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

is  a  separate  resistance  that  may  be  used  to  shunt  either  /S^  or  $2, 
thereby  changing  the  resistance  of  either  by  a  known  amount. 

In  taking  a  reading,  the  coil  R  is  placed  as  shown  in  the 
figure,  and  the  sliding  contact  Gr  is  moved  along  the  test  bar 
until  the  galvanometer  shows  no  deflection. 

R  is  then  changed  over  to  shunt  S^  and  a  new  point  on  the 
bar  at  which  Gr  rests  without  causing  a  galvanometer  deflection 
is  found.  The  resistance  of  the  length  of  the  bar  measured 
between  the  two  balance  points  is,  as  is  evident  from  the 
description  of  the  Carey-Foster  method,  the  difference  between 
the  resistance  of  either  of  the  like  coils  /S^  or  Sa  alone,  and  when 
the  same  is  shunted  by  R.  Means  are  provided  so  that  R  may 

il 


FIG.  94. 


be  shifted  from  one  position  to  another  without  opening  the 
protective  casing. 

THE   MATTHIESSEN    AND    HOCKIN   BRIDGE. 

The  Matthiessen  and  Hockin  method  of  measuring  low  resist- 
ances consists  in  connecting  up  a  standard  low  resistance,  the 
unknown  one,  a  straight  resistance  wire  whose  resistance  per 
unit  of  length  has  been  determined,  and  the  source  of  current, 
all  as  shown  in  Fig.  96.  A  galvanometer  has  its  terminals 
attached  to  separate  contacts ;  the  upper  one  of  which  can 
be  used  to  make  contact  between  the  extremities  of  the 
standard  bar,  S,  and  the  unknown  resistance,  X\  the  lower  one 
being  movable  along  the  stretched  wire,  which  latter  is  often 


THE   MEASUREMENT   OF   RESISTANCE.  127 

the  wire  of  an  ordinary  slide-wire  bridge.  The  upper  galvanom- 
eter terminal  being  placed  at  the  left-hand  extremity  of  the 
bar,  S,  the  lower  one  can  be  moved  along  the  slide  wire  until  a 
point  is  reached  where  the  galvanometer  no  longer  shows  deflec- 
tion. The  potential  at  this  point,  A,  is  then  the  same  as  the 
potential  at  the  end  of  the  standard  bar.  The  upper  terminal 
is  then  moved  to  the  other  end  of  the  standard  bar,  and  the 
lower  one  slid  along  the  slide  wire  until  the  galvanometer  again 
shows  no  current.  This  second  balance  point  is  lettered  B  in 
the  figure.  In  a  similar  way,  the'  points  C  and  D  are  found 
on  the  slide*  wire  at  which  the  potentials  are  the  same  as  the 
potentials  at  the  ends  of  the  unknown  resistance.  The  value 
of  X  may  then  be  calculated  directly  from  the  relation, 

S       AB 

X  ==  OD- 

RAIL    BOND    RESISTANCES. 

In  the  ordinary  electric  trolley  system,  the  current  led  to  the 
car  through  the  overhead  trolley  wire  is  returned,  after  passing 


FIG.  95. 


through  the  motors,  by  the  tracks,  which  have  fish-plates  to 
form  the  mechanical  union  between  rail  ends  and  "  bonds " 
consisting  of  more  or  less  flexible  electrical  conductors  secured 
to  each  rail  end  to  make  the  electrical  union.  As  the  number 
of  rail  joints  is  large  in  even  a  small  system,  it  is  important 
that  the  bonds  bridging  them  shall  make  good  contact,  as  other- 
wise there  will  be  a  considerable  useless  expenditure  of  elec- 
trical energy  in  forcing  the  current  through.  It  is  seldom 
possible  to  inspect  the  bonds  visually  in  order  to  deteimine 
whether  or  not  they  are  still  firmly  attached  to  the  rail  ends, 
and,  even  if  it  were,  a  rigid  mechanical  connection  is  not  neces- 
sarily a  good  electrical  one. 

It  is,  as  a  rule,  impossible  to  measure  the  resistances  of  a  bond 


128       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

by  passing  a  known  current  through  it  and  observing  the  drop 
across  it,  as  cars  that  are  in  operation  cause  a  constantly  vary- 
ing, and,  of  course,  unknown,  current  to  flow.  Practical  devices 
for  the  measurement  of  bond  resistances  utilize  the  varying 
current  normally  flowing  through  the  rail  and  bond,  and  take 
advantage  of  the  fact  that,  however  the  current  and  the  con- 
sequent drops  across  the  resistance  offered  by  the  bond  and 
that  offered  by  a  standard  length  of  rail  vary,  the  ratio  of  these 
drops  to  one  another  remains  constant. 

In  the  Conant  bond  tester,  the  drops  are  taken  by  means  of 
three  chisel-ended  pikes  which  are  struck  into  the  rail  faces  by 
the  operator  and  his  assistant.  The  drop  of  potential  across  the 
bond  between  one  pike  and  the  center  one  is  compared  with  the 
drop  over  a  length  of  solid  rail  measured  between  the  center 


pike  and  the  remaining  one  by  means  of  a  device  suspended  from 
the  observer's  shoulders.  The  instrument  consists  of  a  box  con- 
taining clockwork-driven  interrupter  which  periodically  makes 
and  breaks  the  circuits.  The  latter  are  connected  in  opposition 
electrically,  and  hence,  if  the  resistance  of  the  bond  and  of  the 
length  of  solid  rail  included  between  the  contact  points  are 
alike,  no  current  will  flow,  and  the  telephone  receiver  that  the 
observer  has  at  his  ear  will  emit  no  sound.  If  the  receiver  does 
"  click,"  the  assistant  moves  his  chisel  along  until  silence 
ensues,  whereupon  the  bond  resistance  is  known  to  be  the 
same  as  that  of  the  length  of  rail  between  his  contact  and  the 
center  one. 

Two  other  forms  of  bond  testers  are  shown  in  Figs.  98  and 
99  respectively. 

In  the  first,  three  contact  points   are    carried  by  a  bar  of 


THE  MEASUREMENT  OF  RESISTANCE. 


129 


springy,  non-conducting  material  so  arranged  that  they  scrape 
a  bright  surface  for  themselves  when  being  placed  in  position. 
The  center  contact  is  independently  spring-supported,  so  as  to 
insure  contact  of  all  three  points  even  if  the  rails  should  be 
worn  and  the  surfaces  not  in  the  same  plane.  The  drops  due 
to  the  passage  of  the  regular  line  current  through  the  standard 
length  of  rail  B  C  and  the  bond  B  A  respectively,  are  indi- 
cated by  a  pair  of  milli voltmeters  that  are  electrically  connected 
to  the  points  of  contact  by  suitable  leads.  The  two  millivolt- 
meters  are  built  on  one  base  for  convenience  in  transportation 
and  in  making  observations  ;  and  the  one  that  is  used  to  measure 
the  drop  across  the  bond  terminals  is  made  with  two  ranges ; 
one  high  one,  normally  in  circuit,  and  intended  to  prevent  the 


W/W//tfmvm^^ 

FIG.  98. 

instrument  from  burning  out  should  the  bond  be  broken  and 
the  E.M.F.  across  it  consequently  very  high,  the  other  for  ob- 
taining an  accurate  reading  of  the  drop  after  the  first  reading 
shows  it  to  be  within  the  capacity  of  the  more  sensitive  scale. 
The  change  from  the  low  sensibility  to  the  high  one  is 
effected  by  depressing  a  spring-controlled  button  conveniently 
located  at  the  side  of  the  instrument.  The  millivoltmeter 
for  taking  the  drop  on  the  standard  length  of  rail  is  a 
plain  single-scale  instrument.  After  taking  a  reading,  the 
resistance  of  the  bond  may  be  figured,  if  desired,  from  the 
obvious  fact  that  the  resistance  of  the  bond  is  to  the  resistance 
of  the  standard  length  of  rail  as  the  drop  across  the  bond  is  to  the 
drop  across  the  standard  length  of  rail.  The  double  millivolt- 


130       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

meter  is  usually  used  mounted  on  a  tripod  for  the  sake  of 
having  a  steady  foundation,  but  it  may  be  used  suspended  from 
the  observer's  neck,  if  desired.  This  form  of  bond  tester  is 
convenient  in  that  it  may  also  be  used  as  a  direct  current 
ammeter  if  a  suitable  shunt  be  supplied  for  use  with  the  milli- 
volt scale,  and  as  a  direct  current  voltmeter  if  a  suitable  multi- 
plier be  supplied  for  use  with  the  volt  scale.  It  is  also  con- 
venient for  making  the  so-called  "  bar  to  bar  "  test  on  armatures, 
in  which  case  one  of  the  two  millivoltmeter  movements  may 


FIG.  99. 


be  used  to  show  the  drop  across  the  individual  commutator 
segments ;  the  other,  being  used  to  make  sure  that  the  test  cur- 
rent strength  remains  constant,  by  connecting  it  in  shunt  to  the 
wire  through  which  that  current  is  passing. 

The  second  form  of  bond  tester  is  a  direct  reading  instru- 
ment, showing  directly  on  a  scale  the  resistance  of  the  bond 
under  test  in  terms  of  the  number  of  feet  of  rail  length  having 
an  equivalent  resistance,  but  it  cannot  be  used  as  a  voltmeter  or 
ammeter.  An  illustration  of  the  instrument  itself  is  given  in 
Fig.  99  ;  the  instrument  in  use  is  shown  in  Fig.  100.  Contact 
with  the  rail  is  made  with  a  contact  bar  like  that  used  with  the 


THE  MEASUREMENT  OF  RESISTANCE. 


131 


apparatus  described  above,  the  contact  pieces  themselves  being 
short  sections  of  hack  saw  blades,  which  have  hard,  sharp  points, 
and  are  easily  and  cheaply  renewed  when  dulled. 

The  bar  has  an  upright  at  its  center,  so  that  the  observer  may 
manipulate  it  conveniently. 
The  bond  tester  proper  is  a 
modified  bridge  which  uses  the 
standard  rail  length  as  the 
standard  resistance,  the  bond  as 
the  unknown  resistance,  and  the 
current  normally  flowing  in  the 
rail  as  the  source  of  current. 
In  the  instrument  casing  are  the 
ratio  arms  and  the  galvanometer 
for  showing  balance.  A  con- 
venient feature  of  this  form  of 
bond  tester  is  that  the  observer 
may  select  any  rail  length  that 
he  pleases,  as  that  which  a  bond 
must  not  exceed  if  it  is  to  be 
passed  as  "good," and, by  simply 
setting  the  large  needle  to  that 
length  on  the  scale,  observe  the 
instant  that  the  contact  bar  is 
put  on  the  rail  whether  the 
bond  is  of  higher  or  lower  resistance,  and  hence  to  be  con- 
demned or  to  be  passed. 

The  galvanometer  in  these  instruments,  while  sufficiently 
sensitive  to  enable  the  bond  resistance  to  be  read  within  a  few 
inches  of  rail  length  even  if  but  a  single  car  is  in  operation,  is 
robust  enough  to  stand  the  potential  due  to  a  drop  of  over  two 
volts  across  the  bond  without  injury. 

HIGH    RESISTANCES. 

Direct  Deflection  Method. 

One  of  the  most  common  methods  of  measuring  a  high  re^ist- 
ance  is  to  use  a  sensitive  reflecting  galvanometer  and  a  source 
of  high  E.M.F.,  the  latter  being  usually  furnished  by  a  set  of 
100  or  more  small  batteries,  mounted  in  a  carrying  case.  The 
galvanometer  should  be  provided  with  a  shunt,  to  vary  its  sen- 


FIG.  100. 


132       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

sibility ;  and  a  standard  high  resistance,  usually  of  100,000  ohms 
value,  should  also  be  available.  The  method  of  procedure  is, 
first,  to  ascertain  the  sensibility  of  the  galvanometer  by  placing 
the  100,000  ohms  resistance  in  series  with  it,  shunting  the  gal- 
vanometer with  the  highest  ratio  shunt,  and  then  applying  the 
battery.  If,  with  a  shunt  decreasing  the  sensibility  of  the  gal- 
vanometer to  one  ten-thousandth  of  the  full  sensibility  and  100 
cells  of  battery,  the  standard  100,000  ohms  resistance  placed  in 
series  with  the  galvanometer  results  in  a  galvanometer  deflec- 
tion of  forty  scale  divisions,  the  deflection  through  one  meg- 
ohm with  the  same  shunt  ratio  and  the  same  battery  would 
evidently  be  four  scale  divisions,  and  with  the  same  battery,  but 
a  unity  ratio  shunt,  40,000  scale  divisions,  if  such  were  within 
the  capacity  of  the  apparatus.  If,  now,  the  galvanometer  be  of 
a  type  in  which  the  deflections  are  in  direct  proportion  to  the 
current  flowing  through  the  instrument,  we  have  an  equipment 
in  which  the  existing  battery  would  give  40,000  scale  divisions 
deflection  through  one  megohm  in  series  with  the  galvanometer, 
and  conversely  one  scale  division  deflection  with  40,000  meg- 
ohms in  series  with  the  galvanometer.  If,  therefore,  the  un- 
known resistance  be  inserted  in  the  battery  circuit,  its  value 
may  be  calculated  directly  from  the  deflection  which  the  gal- 
vanometer shows. 

If  the  order  of  the  resistance  to  be  measured  be  entirely  un- 
known, it  is  advisable  to  use  a  high  ratio  shunt  in  connection 
with  the  galvanometer  when  making  the  initial  readings,  and 
subsequently  to  decrease  the  ratio  until  a  point  is  reached  where 
good  readable  deflections  are  had.  It  is  better  to  use  a  shunt 
for  the  galvanometer  than  to  attempt  to  accomplish  the  same 
end  by  decreasing  the  E.M.F.  applied,  because  the  insulators 
used  to  support  the  terminals  of  the  unknown  resistance  per- 
mit of  a  minute  but  still  appreciable  flow  of  current,  and  the 
resistances  offered  by  them  to  that  flow  are  higher  when  the 
material  is  under  the  small  stress  caused  by  a  low  E.M.F.  than 
when  under  the  more  usual  working  condition  of  a  high  E.M.F. 
It  is  particularly  unsafe  to  assume  that  because,  say,  ten  cells 
give  a  certain  deflection  through  a  given  resistance,  twenty  will 
give  twice  that  deflection,  as  the  small  batteries  used  in  high  re- 
sistance testing  work  are  notoriously  unreliable,  and  it  is  not 
often  that  any  two  of  them  will  give  the  same  potential  after 
they  have  been  out  of  the  maker's  hands  for  any  length  of  time. 


THE  MEASUREMENT  OF  RESISTANCE. 


133 


GUARD    WIRES. 

In  a  great  many  cases  the  resistance  to  be  measured  is  that 
offered  by  the  protective  coating  of  a  wire,  and  it  is  then  usual 
to  immerse  the  coil  of  wire  in  a  metal-lined  tank  which  can  be 
filled  with  water,  the  coil  terminals  being  left  projecting  above 
the  surface.  The  resistance  of  the  insulating  coating  on  the 
wire  is  so  high  compared  with  that  of  the  path  through  the 
large  volume  of  water  present,  that  the  latter  is  negligible,  and 
the  resistance  measured  between  the  wire  and  the  tank  lining 
may  be  taken  as  the  resistance  of  the  insulation. 

The  insulation  resistance  is  often  of  so  high  a  value  that  the 


FIG.  101. 

leakage  path  offered  to  the  current  over  the  surface  of  the  in- 
sulating material  from  the  point  where  the  wire  emerges  from 
the  surface  of  the  water  in  the  tank,  shunts  an  appreciable 
fraction  of  the  current  and  would,  hence,  introduce  errors 
unless  allowed  for  or  prevented.  To  allow  for  it  is  extremely 
difficult,  as  its  value  varies  constantly  with  atmospheric 
and  other  conditions.  It  may  be  largely  prevented  by  clean- 
ing and  drying  the  exposed  ends  with  alcohol,  but  is  Hm- 
inated  much  more  satisfactorily  by  using  a  "  guard  wire," 
as  illustrated  in  Fig.  101.  The  guard  wire  is  simply  a  few 
turns  of  fine  copper  wire  wound  over  the  surface  of  the  insula- 
ting material  near  the  point  where  this  is  cut  away  to  allow  the 


134       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

attachment  of  the  main  test  wires.  The  wire  connection  is  led 
past  the  galvanometer  and  direct  to  the  batteries,  so  that  any 
leakage  current  flowing  over  the  surface  of  the  wire  insulation 
will  be  carried  around  the  galvanometer  and  back  to  the  battery 
again  without  affecting  the  galvanometer  indications. 

GALVANOMETER   AND  VOLTMETER   METHOD. 

When  the  source  of  E.M.F.  that  is  available  for  making  the 
resistance  measurements  is  of  uncertain  and  fluctuating  value, 
a  galvanometer  can  still  be  used  to  determine  the  value  of  the 
resistance,  but  the  services  of  a  commercial  voltmeter  must  then 
be  called  into  requisition  also. 

Fig.  102  shows  the  connections.  The  voltmeter  is  attached 
so  that  it  indicates  the  potential  between  the  terminals  applied 
to  the  unknown  resistance,  and  the  galvanometer  is  con- 

T 

^a^+ AMAAAA/WWWWWWWWWWWWWVW 


FIG.  102. 

nected  in  series  with  the  latter  in  the  usual  way.  The 
calibration  of  the  galvanometer,  namely,  the  number  of  amperes 
that  must  flow  through  it  in  order  to  produce  one  scale  division 
deflection,  must  be  known,  as  must  likewise  the  resistance  of 
the  galvanometer. 

The  galvanometer  is  used  as  an  ammeter  to  measure  the 
strength  of  the  current  which  flows  through  the  insulation,  and 
the  value  of  the  resistance  is  calculated  from  Ohm's  law;  it 
being  remembered,  however,  that  the  voltage  indicated  by  the 
voltmeter  is  that  existing  between  the  terminals  of  the  unknown 
resistance  and  the  galvanometer  connected  in  series  with  one 
another,  and  not  that  of  the  unknown  resistance  alone,  so  the 
result  of  the  simple  application  of  Ohm's  law  gives  a  resistance 
value  equal  to  the  sum  of  the  unknown  resistance  and  that  of 
the  galvanometer.  To  obtain  final  results,  therefore,  it  is 
necessary  to  subtract  the  galvanometer  resistance  from  the  value 
derived  as  above.  It  is  not  feasible  to  change  the  voltmeter 


THE  MEASUREMENT  OF  RESISTANCE.  135 

connections  so  that  the  voltage  across  the  unknown  resistance 
alone  is  indicated,  as  the  galvanometer  would  then  show  the 
current  flowing  through  the  circuit  composed  of  the  unknown 
resistance  and  that  of  the  voltmeter  connected  in  parallel,  and 
the  latter  is  so  low  in  comparison  to  the  former,  that  an  error 
of  a  small  fraction  of  a  per  cent  in  measuring  the  total  current 
flowing  would  make  an  error  of  many  per  cent,  when  the  cur- 
rent flowing  through  X  is  computed  by  subtracting  the  known 
voltmeter  current  from  the  indicated  total  value. 

LEAKAGE   METHOD. 

The  resistance  of  the  covering  of  an  insulated  wire  may  be 
measured  by  comparing  the  charge  that  it  will  give  off  immedi- 
ately after  being  disconnected  from  a  source  of  charging  E.M.F., 
and  the  charge  that  remains  after  it  has  been  disconnected 
from  that  source  for  a  known  period,  the  theory  being  that  the 
difference  has  leaked  through  the  covering  at  a  rate  that,  of 
course,  varies  with  the  elapsed  time.  The  preferred  pro- 
cedure in  making  a  test  according  to  this  method  is  to  immerse 
the  coil  of  wire  in  a  tank  of  water,  one  end  being  first  carefully 
sealed,  thus  forming  a  condenser  in  which  the  inner  coating  is 
the  conductor,  the  outer  coating  is  the  water,  and  the  in- 
sulating covering  the  dielectric. 

This  condenser  is  first  charged  by  applying  a  source  of  con- 
stant E.M.F.,  and  is  then  allowed  to  stand  for  a  measured 
number  of  seconds,  say  thirty.  It  is  then  discharged  through 
a  ballistic  galvanometer  and  the  throw,  D^  noted.  The  operation 
is  then  repeated  with  the  same  charging  circuit,  the  period 
during  which  leakage  through  the  insulation  is  allowed  to  take 
place  after  disconnecting  the  charging  source  being,  however, 
made,  say  sixty  seconds.  Let  the  second  deflection  be  D2.  If 
the  two  observed  deflections  were  not  too  great,  the  resistance 
in  megohms  of  the  insulating  coating  is 

R=-  * 

O  x  log,.  J  x  2.303 

The  foregoing  method  must  be  used  with  discretion,  because 
if  the  wire  insulation  is  of  a  material  with  high  electric  absorb- 
tive  or  "  soakage  "  qualities,  the  results  will  be  misleading. 


136       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

DROP  OF  POTENTIAL  METHOD. 

If  the  standard  resistance  /Sr  and  the  unknown  one  X  be  con- 
nected together  in  series  and  current  passed  through  them  from 
a  battery,  B,  as  in  Fig.  103,  a  reflecting  electrometer,  or  electro- 
static voltmeter,  may  be  used  to  determine  X  in  terms  of  S  by 
connecting  it  first  to  the  terminals  of  >ST,  and  then  to  those  of  X  ; 
whereupon  the  result  is  at  once  obtained  in  a  manner  analogous 
to  that  mentioned  on  page  117.  No  correction  need  be  made 
in  this  instance  for  the  resistance  of  the  device  that  indicates 
the  potential,  as  this  is  infinitely  high  as  compared  with  the 
resistance  of  the  objects  under  measurement. 

A  Thompson  or  D'Arsonval  ballistic  galvanometer  can  be 
used  in  place  of  the  electrostatic  instrument  by  charging  a 
condenser  first  from  the  drop  across  $,  discharging  it  through 
the  galvanometer  and  noting  the  throw,  and  then  by  Repeating 
the  operation  with  X,  in  which  case  the  throws  are,  in  the  ratio 
of  the  resistances. 

EVERSHED    OHMMETER. 

This  is  an  instrument  for  measuring  moderately  high  resist- 
ances, which  shows  directly  from  the  position  of  a  needle  swing- 


FlG.  103. 

ing  over  a  calibrated  scale  the  value  in  ohms  of  the  resistance 
under  measurement.  It  consists  of  two  coils  arranged  with 
their  axes  at  right  angles  to  each  other,  one  of  which  coils  is 
connected  in  series  with  the  source  of  current  and  the  resistance 
to  be  measured,  and  the  other,  like  a  voltmeter,  across  the  line 
from  which  current  is  supplied.  At  the  point  of  intersection  of 
the  coil  axes  there  is  suspended,  so  as  to  be  freely  movable,  a 


THE  MEASUREMENT  OF  RESISTANCE.  137 

short  magnetized  steel  needle.  If  the  resistance  be  infinitely 
high,  no  current  will  flow  through  the  series  coil  of  the  instru- 
ment ;  the  needle  will  be  influenced  by  the  potential  coil  only 
and  assume  a  position  at  right  angles  to  its  axis.  If,  on  the 
other  hand,  the  resistance  be  zero,  and  the  current  obtained  from 
a  source  whose  internal  resistance  is  fairly  high,  current  will 
flow  through  the  series  coil  only,  there  will  be  practically  no 
difference  of  potential  between  the  points  of  attachment  of  the 
potential  coil,  and  therefore  the  needle  will  assume  a  position 
parallel  to  the  axis  of  the  series  coil.  With  finite  resistances 
the  needle  is  evidently  influenced  by  the  joint  action  of  the 
fields  of  the  two  coils,  tending  to  swing  toward  the  infinity 


FIG.  104. 


mark  when  the  current  is  low  and  the  potential  high  and  vice 
versa. 

In  the  actual  apparatus  the  source  of  current  is  a  small  hand- 
driven  dynamo  having  permanent  magnet  fields,  namely,  a  mag- 
neto which  when  driven  at  a  reasonably  constant  speed  sup- 
plies  rectified  alternating  current  at  potentials  of  from  100  volts, 
in  the  case  of  instruments  designed  to  measure  resistances  up  to 
about  5  megohms  to  500  volts  for  meters  measuring  up  to 
500  megohms.  Theoretically,  the  calibration  of  this  ohm  meter 
can  be  calculated  from  the  geometrical  dimensions  of  the  appa- 
ratus, the  number  of  turns  of  wire,  etc.,  but  practically  it  is 
better  to  graduate  the  scales  empirically  by  comparison  with 
resistances  of  known  value.  A  diagram  of  the  connections  of 
the  instrument  is  shown  in  Fig.  104. 

In  the  early  form  of  this  ohmmeter,  the  moving  needle  was 
of  steel  magnetized  as  above  mentioned,  but  this  was  open  to  the 
objection  that  the  needle  was  readily  influenced  by  comparatively 


138       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

feeble  stray  magnetic  fields,  even  those  of  the  hand  generator 
which  supplied  the  current.  In  the  more  modern  form  of  appa- 
ratus a  soft  iron  needle  is  employed,  which,  while  resulting  in  a 
shorter  scale  because  the  zero  must  be  placed  in  the  center  in- 
stead of  at  one  end,  enables  the  user  to  eliminate  the  effect  of 
stray  fields,  by  reversing  the  current  and  taking  the  mean  of  the 
observed  indications.  The  current  reversal  is  readily  effected 
by  turning  the  crank  in  an  opposite  direction,  thus  reversing 
the  direction  of  the  rotation  of  the  magneto  armature. 

SPECIAL  CONDITIONS. 
The  foregoing  outline  of  methods  of  measuring  resistances  of 


FIG.  105. 


different  values  treats  only  of  the  measurement  of  simple  cir- 
cuits, such  as  the  resistance  of  a  metallic  body,  or  a  poor  con- 
ductor in  which  no  disturbing  factors,  such  as  local  E.M.F.'s 
exist.  In  practice,  however,  disturbing  E.M.F.'s  are  frequently 
present,  being  either  existent  before  the  measurement  is  at- 
tempted, as  in  the  case  of  a-  battery,  or  being  set  up  by  the  passage 
of  the  current  employed  in  measuring  the  resistance,  as  in  the 
case  of  an  electrolyte.  These  E.M.F.'s  tend  to  cause  currents 
to  flow  in  the  network  of  conductors,  which  are  ordinarily  nec- 
essary in  measuring  resistances,  and  make  the  indications  of  the 
galvanometer  or  telephone  receiver,  used  as  the  current  detector, 
erroneous.  In  the  following  we  will  take  up  the  methods  of 
measuring  the  resistances  of  circuits  which  contain  these  dis- 
turbing elements  and  are  frequently  met  with  in  practice. 


THE  MEASUREMENT  OF  RESISTANCE.  139 

RESISTANCE    OF    ELECTROLYTES. 

Any  liquid  not  a  melted  metal,  such  as  mercury,  fused  lead, 
etc.,  which  is  a  conductor  of  electricity,  is  an  electrolyte,  and  all 
electrolytes  are  decomposed  when  current  flows,  the  decomposi- 
tion setting  up  an  E.M.F.  opposing  that  of  the  source  that  forces 
the  current  through  it.  This  fact  makes  it  impossible  to  meas- 
ure the  resistance  of  an  electrolyte  with  the  ordinary  Wheat- 
stone  bridge  arrangement,  lief  erring  to  Fig.  105,  if  the  X  arm 
of  the  elementary  Wheatstone  bridge  shown  in  the  figure  con- 
tains in  itself  a  source  of  E.M.F.  the  correct  value  of  jS,  which 

must  be  inserted  to  make  the   ratio  -^  =  -^  hold  good,  is  no 

.o        ^A. 

longer  attained  when  the  galvanometer  shows  no  deflection,  as, 
where  an  ordinary  resistance  would  keep  the  difference  of 
potential  between  the  junctions  of  AB  and  SX  alike,  a  source, 
X,  that  contains  in  itself  a  source  of  potential  difference  will 
cause  a  flow  of  current  through  the  bridge  network  under  the 
same  circumstances  and  show  a  galvanometer  deflection. 

Kohlrausch  Bridge. 

Tn  measuring  the  resistance  of  an  electrolyte,  one  way  of 
overcoming  this  point  is  to  use,  instead  of  the  direct  current 
which  calls  forth  the  counter  E.M.F.  of  the  electrolyte,  an  alter- 
nating current  with  the  current  reversals  succeeding  each  other 
so  rapidly  that  decomposition  at  either  pole  is  immediately  re- 
composed  and  the  disturbing  E.M.F.  set  up  in  one  direction,  off- 
set by  an  immediately  following  and  opposite  one. 

Kohlrausch  first  suggested  the  above  method  and  used  for 
the  measurement  of  the  resistance  of  electrolytes  an  ordinary 
slide- wire  bridge  of  the  type  shown  in  Fig.  72,  obtaining  the 
current  applied  to  the  slide  wire  terminals  from  the  secondary 
winding  of  an  induction  coil  actuated  by  a  battery.  If  the 
induction  coil  core  be  of  hard  iron,  or  even  steel,  the  secondary 
current  becomes  very  nearly  a  pure  alternating  current  with 
smooth,  symmetrical  waves,  a  feature  that  is  necessary  to  secure 
good  results. 

The  ordinary  Thompson  or  D' Arsonval  types  of  galvanometers 
cannot  be  used  as  current  detectors  with  this  form  of  bridge 
because  they  respond  only  to  direct  current. 

Their  place  is  usually  taken  by  a  telephone  receiver  and  when 


140       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

the  sliding  contact  is  moved  along  until  a  point  is  reached 
where  the  receiver  no  longer  gives  forth  a  humming  sound,  the 
value  of  the  resistance  of  the  electrolyte  can  be  calculated  or 
read  off  exactly  as  in  the  case  of  the  same  instruments  used  with 
direct  current  for  the  measurement  of  ordinary  resistances. 

The  frequency  of  the  alternating  current  used  must  be  high, 
because  if  the  current  reversals  follow  one  another  too  slowly, 
polarization  may  take  place. 

With  the  frequency  obtainable  with  the  interrupter  of  an 
ordinary  induction  coil,  fairly  good  results  are  obtainable,  but  it 
is  claimed  by  Duddell  that  the  frequency  must  attain,  at  least, 


FIG.  106. 


10,000  alternations  per  second  if  polarization  errors  are  to  be 
entirely  eliminated. 

No  orthodox  Kohlrausch  bridges  are  made  in  this  country, 
but  the  Hanchett-Sage  ohmmeter  described  on  page  107  is 
often  used  for  such  work.  A  special  model  of  this  instrument 
with  the  induction  coil  for  supplying  the  alternating  current 
permanently  fastened  in  the  cover,  and  with  the  wiring  con- 
nections self-contained,  is  shown  in  Fig.  106.  The  galvanometer 
shown  as  built  into  the  instrument,  responds  to  direct  current 
only,  and  is  used  for  other  tests,  it  being  possible  to  throw  either 
it  or  the  telephone  receiver  into  circuit  to  act  as  the  current 
detector  by  means  of  a  switch  provided  for  that  purpose. 

Secohmmeter  Method. 

A  galvanometer  which  responds  to  direct  current  only  can  be 
used  when  the  direction  of  the  current  flowing  through  the  elec- 


THE  MEASUREMENT   OF  RESISTANCE. 


141 


FIG.  107. 


trolyte  is  being  continuously  reversed,  if  the  connections  to  the 
galvanometer  be  simultaneously  reversed.  The  apparatus  for 
bringing  about  these  two  reversals  simultaneously  is  the  secohm- 
meter  illustrated  in  Fig.  107.  The  device  consists  of  a  commu- 
tator, rotated  by  hand  by  means  of  a  crank,  and  having  bearing 
thereon,  contact  brushes  through  whose  aid  the  direction  of  the 
current  flowing 
through  both 
circuits  is  con- 
tinuously re- 
versed. It  is 
necessary  to 
rotate  the  handle 
at  a  high  speed, 
as  the  current 
reversals  must, 
as  before  ex- 
plained, succeed 
each  other  with 

sufficient  rapidity  to  annul  the  polarization  effect.  The  galvanom- 
eter movement  must  be  heavy,  so  as  to  possess  inertia  sufficient 
to  prevent  its  swinging  back  and  forth  in  an  attempt  to  keep 
step  with  the  pulsations  of  the  current.  With  these  conditions 
fulfilled,  the  resistance  of  an  electrolyte  may  be  measured  by 
the  Wheatstone  bridge  method,  and  a  secohmmeter  with  the 
same  ease  as  that  of  any  metallic  circuit. 

Stroud  and  Henderson  Method. 

This  is  entirely  different  from  any  of  the  foregoing,  and  con- 
sists of  an  ingenious  modification  of  the  ordinary  Wheat- 
stone  bridge.  Referring  to  Fig.  108,  T^  and  T2  are  two  tubular 
vessels  containing  the  electrolyte,  similar  as  to  diameter  and 
nature  of  terminals,  but  differing  in  length  by  a  known  amount. 
P  and  <?,  the  two  other  arms  of  the  bridge,  are  made  of  very 
high  resistance,  say  20,000  ohms  each,  this  being  desirable,  as 
the  resistance  of  electrolytes  is  high,  and  it  is  always  desirable 
in  Wheacstone  bridge  measurements  to  have  the  resistance  of 
the  four  arms  of  the  same  order.  The  galvanometer  should  also 
be  of  the  high  resistance  pattern.  To  obtain  results,  R,  which 
is  an  adjustable  resistance,  is  manipulated  until  the  galvanometer 


142       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


shows  no  current,  whereupon  the  ratio 


T 


^ 

-f  ±1 


P 

obtains. 


As  the  electrolyte  in  T^  and  T2  is  the  same,  the  polarization 
E.M.F.  of  the  branch  containing  Tl  is  exactly  neutralized  by  the 
polarization  E.M.F.  in  the  branch  T^  and  the  actual  resistance 
per  unit  length  of  column  of  electrolyte  may  be  calculated  from 
the  ratio  just  given. 

In  measuring  the  resistance  of  an  electrolyte  by  any  of  the 
foregoing  methods  the  liquid  is  usually  placed  in  a  U-shaped  glass 
vessel,  as  shown  in  Fig.  109.  The  cubic  contents  per  unit  of 
length  of  tube  are  carefully  determined  and  the  tube  length 
itself  is  measured  with  care.  The  tube  ends  are  made  as  large 


FIG.  108. 


cups  in  order  to  allow  of  the  introduction  of  electrodes  of  con- 
siderable size.  With  almost  all  electrolytes  the  electrodes  must 
be  of  platinum,  sometimes,  in  order  to  obtain  the  large  area  that 
is  necessary  to  give  an  efficient  contact  between  the  electrode 
and  the  liquid,  of  corrugated  platinum  sheet.  It  is  more  usual, 
however,  to  use  an  electrode  of  spongy  platinum,  or,  still  better, 
sheet  platinum  coated  with  a  deposit  of  platinum  black.  In  all 
drop  of  potential  methods  of  measurement  it  is  desirable  to  use 
a  separate  pair  of  electrodes  to  make  contact  with  the  column 
of  liquid  at  a  known  distance  apart  in  order  to  eliminate  an 
error  due  to  the  contact  resistance  between  the  main  termi- 
nals and  the  electrolyte. 


THE  MEASUREMENT  OF  RESISTANCE.  143 

Instead  of  determining  the  volume  of  the  contents  of  an  elec- 
trolyte tube,  and  from  this,  by  measuring  the  length  of  a  section, 
the  average  cross-section  of  a  column  of  the  liquid,  it  is  usually 
much  more  convenient  to  obtain  the  resistance  in  terms  of  that 
of  a  liquid  whose  resistance  per  unit  volume  is  known.  Mer- 
cury is  often  used  as  the  standard  in  this  way,  the  tube  being 
first  filled  to  a  certain  level  with  this  and  the  resistance  meas- 
ured, the  performance  being  then  repeated  with  the  same  volume 
of  the  liquid  under  test.  The  ratio  of  the  results  is  then  the 
ratio  of  the  specific  resist- 
ance of  mercury  to  that 
of  the  solution  being  in- 
vestigated. A  standard 
solution  that  is  itself  an 

1      ,  U  FlG-   109' 

electrolyte  is  even  better 

than  mercury.  Favorite  liquids  of  this  class  are  sodium  chlo- 
ride (Na  Cl),  a  solution  of  which  having  a  specific  gravity  of 
1.201  has  a  resistance  of  4.66  ohms  per  cubic  cm.  at  18°  C.  and 
a  temperature  coefficient  of  .0234,  and  copper  sulphate  (Cu  SO4), 
a  solution  of  which  having  a  specific  gravity  of  1.208  has  a  re- 
sistance of  29.37  ohms  per  cubic  cm.  at  18°  C.  and  a  tempera- 
ture coefficient  of  .0241  (both  according  to  G.  Wiedermann). 

One  point  to  be  borne  in  mind  in  connection  with  methods 
using  alternating  current  and  a  Wheatstone  bridge  network  of 
conductors  is  that  the  resistance  coils  and  wires  forming  the 
four  arms  of  the  bridge  must  be  arranged  so  as  to  have  no 
inductance  and  no  capacity,  because,  except  in  the  almost  im- 
possible event  that  the  inductances  and  capacities  are  all  alike, 
the  different  time  constants  of  the  different  branches  will 
throw  the  currents  in  them  out  of  step,  and  it  will  be  impos- 
sible to  obtain  any  balance  at  all.  This  is  one  reason  why  the 
slide-wire  type  of  bridge  is  usually  employed,  a  straight 
stretched  wire  having  negligible  capacity  and  inductance. 

Ayrton  and  Perry  Method. 

In  the  Ayrton  and  Perry  method  of  measuring  the  resistance 
of  an  electrolyte,  the  liquid  is  poured  into  a  containing  vessel, 
shown  in  Fig.  110,  and  current  passed  through  it  with  the  aid 
of  the  platinum  wires  projecting  from  the  sealed  ends  of  glass 
tubes  immersed  in  the  liquid.  A  resistance  in  the  circuit 


144       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

enables  the  strength  of  the  current  to  be  regulated,  and  platinum 
wires  sealed  into  the  ends  of  two  other  glass  tubes,  W  and  TF, 
are  used  to  make  connection  with  a  reflecting  electrometer. 

As  the  electrometer  is  of  infinite  resistance,  it  draws  no 
current  through  the  contacts,  W  and  TF",  hence  there  is  no 
polarization,  and  the  electrometer  shows  the  true  difference  of 
potential  between  these  points.  From  this  and  the  known 
strength  of  the  current  flowing  through  the  electrolyte,  as 
indicated  by  the  milliammeter  in  the  supply  circuit,  the  resist- 
ance may  at  once  be  calculated. 

Hering^s  Liquid  Potentiometer. 

A  modification  of  and  improvement  on  the  foregoing  method 
has  been  described  by  Hering.  (See  Transact,  of  the  A.  I.  E.  E., 


FIG.  110. 

Feb.,  1902.)  In  this  a  trough  of  known  cross-sectional  area  is 
used  to  contain  the  electrolyte,  and  current  is  passed  through 
the  solution  by  means  of  plates,  a  and  5,  immersed  therein,  as 
shown  in  Fig.  111. 

The  strength  of  the  current  flowing  is  measured  by  a  suitable 
ammeter.     There  is  provided  also  a  galvanometer,  6r,  for  detect- 


THE  MEASUREMENT  OF  RESISTANCE. 


145 


ing  the  presence  or  absence  of  current,  and  a  cell  or  group  of 
cells,  E,  of  known  potential.  A  voltmeter,  F,  is  desirable  in 
order  that  the  potential  of  E  may  be  seen  at  a  glance,  but  if 
E  is  a  standard  cell,  it  must,  of  course,  be  dispensed  with.  If 
the  two  plates,  /  and  e,  connected  up  to  the  galvanometer, 
cell  and  voltmeter  as  shown,  be  immersed  in  the  solution  so 
that  the  E.M.F.  between  the  points  of  immersion  is  opposed 
to  that  of  the  ceil  E,  the  distance  between  e  and  /  can  be 
varied  until  the  galvanometer,  6r,  no  longer  shows  a  deflection. 
The  potential  between  e  and  /  is  evidently  that  of  the  cell, 
E,  and  as  the  distance  between  these  points  may  be  read  off 
from  the  scale  shown  on  the  edge  of  the  containing  vat,  the  re- 
sistance of  the  solution  can  be  calculated,  since  we  know  the 
cross-sectional  area  of  the  liquid  column  from  the  size  of  the 


FIG.  111. 

vessel  and  the  depth  of  the  liquid,  the  current  strength  from  the 
instrument  A  and  the  drop  in  potential  due  to  the  resistance 
from  the  E.M.F.  of  E.  According  to  Mr.  Hering,  the  electrodes, 
which  should,  of  course,  be  of  the  same  material,  must  not  be 
attacked  by  the  electrolyte,  or  by  the  products  of  decomposition 
of  the  electrolyte,  before  balance  can  be  attained.  The  latter 
condition  makes  it  impossible  to  use  the  platinum  sponge  or 
platinum  black  electrolytes  which  are  employed  when  making 
the  measurements  by  the  above-mentioned  Kohlrausch  method, 
since  both  store  up  large  quantities  of  gas.  Carbon  was  found 
to  possess  the  same  property  to  an  appreciable  degree,  and  gold 


146        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

seems  to  have  been  the  only  satisfactory  metal.  The  method 
is  of  interest,  as  it  does  not  call  for  any  special  apparatus,  it 
being  possible  to  use  an  ordinary  commercial  pattern  pivoted 
milli voltmeter,  or  shunt  type  ammeter  without  its  shunt,  as  the 
galvanometer,  G\ 

INTERNAL    RESISTANCE    OF    BATTERIES. 

In  making  certain  measurements  it  is  necessary  that  the 
internal  resistance  of  the  battery  supplying  the  current  be 
known.  There  is  a  large  number  of  methods  for  ascertaining 
this  quantity,  but  only  a  few  of  these,  which  are  of  easy 
application  with  commercial  apparatus,  will  be  considered. 

Half-Deflection  Method. 

In  a  simple  circuit,  such  as  that  shown  in  Fig.  112,  comprising 
a  battery,  galvanometer,  or  milliammeter,  and  an  external 

R 


FIG-  112. 

resistance,  let  the  resistance  of  the  various  elements  be  called 
j£,  6r,  and  r,  respectively.  If  the  E.M.F.  of  the  battery  be 
called  e,  the  current,  i,  flowing  through  the  whole  circuit,  is 

i  =  • — By  increasing  r,  i  may  be  reduced  to  one 

half  the  original  value,  in  which  case  we  have  -  = , 

2      R  +  G-  +  N 

in  which  N  is  the  new  resistance  of  r.  From  these  two 
equations  we  deduce  the  value  of  R,  R  —  N —  2r —  6r.  This 
method,  which  is  a  very  simple  one,  is  capable  of  giving  results 
of  considerable  accuracy. 

Mance's  Method. 

In  this  method  the  ordinary  Wheatstone  bridge  is  used,  with 
only    two    changes    of    connections ;    namely,    the    battery   is 


THE  MEASUREMENT  OF  RESISTANCE. 


147 


connected  in  the  place  ordinarily  occupied  by  the  unknown 
resistance,  and  in  the  place  ordinarily  occupied  by  the  battery 
there  is  connected  a  key  for  closing  the  circuit.  The  gal- 
vanometer retains  its  ordinary  position.  The  arrangement  is 
shown  in  Fig.  113.  When  the  key,  7T,  is  open,  there  is  a 
current  through  the  galvanometer,  giving  a  definite  deflection, 
which,  as  will  be  explained  presently,  can  be  made  of  convenient 
magnitude.  If  the  key,  K,  be  now  closed,  and  the  deflection  of 
the  galvanometer  remain  the  same,  the  bridge  is  balanced  and 

the  resistance,  x,  of  the  battery,  is    x  =  ?  c.     Should  the  clos- 

o 

ing  of  the  key,  K,  alter  the  deflection  of  the  galvanometer,  the 
resistance  of  the  rheostat,  c,  must  be  altered  until  the  deflection 


FIG.  113. 


is  the  same  with  TTopen  or  closed.  There  is  a  high  resistance, 
.72,  in  series  with  the  galvanometer,  which  latter  is  provided  with 
the  usual  shunt.  By  this  means  the  current  may  be  regulated 
so  that  a  convenient  deflection  is  obtained  while  still  keeping 
the  total  resistance  of  the  circuit  high,  thereby  preventing  the 
running  down  of  the  battery.  With  this  same  end  in  view,  the 
the  ratio  arms,  a  and  5,  are  of  as  high  resistance  as  practicable. 
This  method  when  properly  handled  gives  satisfactory  results, 
but  the  limit  of  accuracy  is  much  less  than  that  of  ordinary 
Wheatstone  bridge  measurements  of  resistance,  because  in 
these  measurements  a  zero  method  is  used,  which  is  limited  in 
accuracy  only  by  the  limit  of  sensibility  of  the  galvanometer, 
while  the  limit  of  accuracy  of  Mance's  method  is  that  of  a 


148       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

scale  reading,  usually  not  greater  than  one  part  in  three  or  four 
hundred.  This,  however,  is  usually  sufficient  in  practice,  for 
the  resistance  of  a  cell  is  a  very  uncertain  quantity  and  liable 
to  change  on  very  slight  provocation.  Mance's  method  is  fully 
as  accurate  as  the  half-deflection  method. 

Method   Using  Alternating   Current. 

If  a  source  of  alternating  current  be  used  in  place  of  the 
usual  direct  current,  the  internal  resistance  of  a  battery  may  be 
measured  by  the  regular  Wheatstone  bridge  method,  provided 
that  the  bridge  arms  are  without  inductance  or  capacity,  and 
that  the  current  detector  is  one  that  responds  to  alternating 
current  only,  and  does  not  indicate  the  presence  of  the  direct 
current  which  the  battery  under  test  will  cause  to  circulate  in 
the  bridge  network.  A  telephone  receiver  fulfills  this  r^quire- 
ment  if  the  galvanometer  key  or  device  corresponding  thereto 
be  kept  closed  during  the  test,  as  the  continuous  current  will 
merely  put  a  steady  stress  on  the  diaphragm,  still  leaving  it 
free  to  vibrate  when  alternating  current  flows.  The  special 
Hanchett-Sage  ohmmeter,  illustrated  011  page  140,  may  be  used 
for  this  test,  in  which  case  the  stylus  must  be  slid  instead  of 
tapped  along  the  slide  wire. 

It  should  be  noted  that  this  test  gives  the  internal  resistance 
of  the  battery  when  the  same  is  delivering  current,  that  is  to 
say,  its  open  circuit  resistance  plus  that  due  to  any  polarization 
that  may  have  taken  place. 

Where  the  galvanometer  employed  responds  to  both  direct 
and  alternating  current,  as,  for  instance,  a  reflecting  electro- 
dynamometer,  it  is  necessary  to  test  two  identical  cells  at  a 
time,  connecting  them  in  opposition  in  the  JTarm  of  the  bridge, 
as  shown  in  Fig.  114,  in  order  that  their  potentials  may  balance 
one  another  and  no  current  be  caused  to  flow  through  the  net- 
work. It  is  evident  that  the  value  of  the  resistance  obtained  is 
double  that  of  a  single  cell. 

It  will  be  noted  that  this  second  method  gives  the  true  in- 
ternal resistance  of  the  cells  under  open  circuit  conditions. 

The  remarks  under  the  measurement  of  the  resistance  of 
electrolytes  as  to  the  necessity  of  a  high  frequency  of  the  alter- 
nations and  that  the  current  must  be  a  truly  symmetrical  one, 
apply  with  the  same  force  to  these  tests. 


THE  MEASUREMENT  OF  RESISTANCE. 


149 


Internal  Resistance  of  Storage  Batteries. 

Where  the  internal  resistance  of  the  battery  to  be  measured 
is  very  low,  as,  for  instance,  in  the  case  of  a  storage  battery,  it 
may  be  measured  very  simply  in  another  way  involving  only 
the  use  of  an  ammeter  and  a  low-reading  voltmeter.  With  the 
latter  the  open  circuit  E.M.F.  of  the  battery  is  first  taken. 
A  heavy  current  is  then  drawn  from  the  battery  and  its  strength 
measured  by  the  ammeter,  the  E.M.F.  at  the  battery  terminals 
being  simultaneously  measured  with  the  voltmeter  as  before. 
This  gives  us  two  equations  connecting  e,  i,  and  r,  and  from  them 

e  —  er 
we    have  —  -.  —  =  r,  where  e  =  open  circuit  voltage,  e'  =  closed 


circuit  voltage,  r  =  resistance,  and  i  =  current.     Similar  meas- 


FIG.  114. 

urements  may,  of  course,  be  made  when  the  cell  is  charging 
instead  of  discharging. 

RESISTANCE    OF    GALVANOMETERS. 

It  is  more  often  necessary  to  know  the  resistance  of  a  gal- 
vanometer than  that  of  the  cells  themselves.  The  ordinary 
methods  of  measuring  medium  resistances,  before  mentioned, 
can  seldom  be  used  for  this  purpose,  as  they  all  call  for  a  bat- 
tery current  which  is  usually  so  high  as  compared  with  the 
capacity  of  the  galvanometer  that  the  latter  would  be  burned 
out  if  any  such  proceeding  were  attempted.  There  are,  how- 
ever, other  ways  of  obtaining  this  information  about  a  galva- 
nometer, the  more  usual  ones  being  as  follows : 


150       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


Half-Deflection  Method. 

This  is  worked  in  the  same  way  as  the  half-deflection  method 
for  determining  the  internal  resistance  of  a  battery;  that  is  to 
say,  by  letting  a  certain  current  flow  through  the  galvanometer 
and  then  inserting  sufficient  additional  resistance  to  bring  the 
galvanometer  deflection  down  to  one  half.  From  the  same 
formulse  given  in  the  above  paragraph  we  evidently  have 
G  =N  —  R  —  2r,  which  may  be  written  Gr  =  N  —  2r,  if  the 
internal  resistances  of  the  battery,  R,  be  negligible,  as  compared 
with  the  resistance  of  r  and  of  the  galvanometer. 

Thompson's  Method. 

If  the  galvanometer  be  inserted  in  one  arm  of  the  Wheat- 
stone  bridge,  as  diagrammatically  illustrated  in  Fig.  115,  alid  for 


FIG.  115. 

the  galvanometer,  usually  inserted  between  E  and  B,  there  be 
substituted  a  contact  key,  the  value  of  the  resistance,  6,  maybe 
varied  until  the  galvanometer  shows  the  same  deflection  whether 
the  key  is  raised  or  depressed.  When  this  state  of  affairs  is 

reached,  the  resistance  of  the  galvanometer  equals  -?-. 

The  same  test  can  be  made  by  substituting  for  the  type  of 
Wheatstone  bridge  in  which  plug  resistances  are  used  the  slide 
wire  form,  in  which  event  the  key  between  E  and  B  is  dis- 


THE  MEASUREMENT  OF  RESISTANCE.  151 

pensed  with,  ABC  becomes  the  bridge  wire,  and  the  point  of 
contact,    B,   is  adjustable  and  forms  the  sliding  contact.     la 

this  case,  also,  the  galvanometer  resistance  equals  — ,  and  since 

the  ratio  of  a  to  b  alone  enters  into  this  equation  the  absolute 
values  of  a  and  b  need  not  be  known. 


CHAPTER   VI. 

MEASUREMENT   OF  CURRENT. 

INSTRUMENTS  for  measuring  electric  currents  may  conven- 
iently be  divided  into  three  classes  ;  namely,  those  suited  for  mea- 
suring direct  currents  only,  those  for  alternating  current  only, 
and  those  that  can  be  used  for  both  direct  and  alternating  current. 

Beginning  with  the  direct  current  instruments,  and  leaving 
aside  purely  laboratory  apparatus,  such  as  the  voltmeter,  the 
first  commercial  apparatus  to  be  considered  would  logically  be 
the  potentiometer.  This  device  has  already  been  minutely  de- 
scribed in  the  chapter  on  laboratory  standards  for  current 
measurement,  and  is  referred  to  here  because  under  favorable 
conditions  it  can  be  used  in  the  commercial  measurement  of 
current  strength. 

By  far  the  greater  proportion  of  instruments  for  the  meas- 
urement of  direct  current  fall  under  another  heading,  and  are 
of  types  in  which  the  current  strength  may  be  read  off  directly 
from  the  position  of  an  indicating  device  relative  to  a  marked 
scale.  Many  of  such  instruments  contain  permanent  magnets, 
upon  whose  constancy  depends  the  constancy  of  the  accuracy 
of  the  indications.  The  class  may  be  divided  into  two  general 
types :  one  in  which  the  winding  through  which  the  current 
to  be  measured  is  passed  is  held  stationary,  while  a  permanent 
magnet,  or  a  soft  iron  magnet  polarized  by  a  stationary  mag- 
netic field,  is  deflected ;  the  other  in  which  the  magnet  is 
stationary  and  the  wire  through  which  the  current  passes  is 
movable. 

FIXED  COIL  INSTRUMENTS. 

The  commercial  apparatus  in  most  extensive  use  falling 
under  the  first  class  indicated  is  of  the  type  developed  by 
Deprez  and  Carpentier  and  by  Ayrton  and  Perry  many  years 
ago.  In  this  a  magnet,  NS,  Fig.  116,  saturates  magnetically 
a  soft  iron  needle,  m,  and  tends  to  hold  the  latter  constantly 
in  the  position  shown,  as  then  there  is  offered  a  minimum 

152 


MEASUREMENT  OF  CURRENT. 


153 


resistance  to  the  flow  of  the  lines  of  force  from  one  pole  of  the 
magnet  to  the  other.  The  coil  of  wire,  CC,  through  which  the 
actuating  current  flows  is  wound  on  a  spool,  so  that  it  forms  a 
solenoid  whose  axis  is  at  right  angles  to  that  of  the  needle. 
Current  flowing  through  this  solenoid  affects  sn,  just  as  the 
coil  of  a  Thompson  galvanometer  (see  page  56)  causes  the 


FIG.  116. 

magnetized  needle  suspended  within  it  to  deflect  and  tend  to 
take  up  a  position  where  its  axis  is  parallel  to  the  axis  of  the 
coil.  An  increased  current  strength  of  course  exerts  an  in- 
creased force  tending  to  deflect  m,  and  the  needle  will  there- 
fore come  to  rest  only  when  this  increased  effort  is  balanced  by 
the  effort  of  the  magnet,  NS,  to  pull  sn  back  to  its  original 
position,  which  effort  evidently  increases  as  the  extremities  of 


154       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


sn  recede  from  the  poles  NtS.  By  suitably  dimensioning  the 
parts  and  shaping  the  polar  faces  of  SN,  the  opposing  force, 
due  to  the  attraction  of  the  fixed  magnet,  may  be  made  to  in- 
crease for  increasing  deflection  at  the  same  rate  as  the  effort 
tending  to  turn  the  needle,  due  to  the  current  flowing  through 
the  coil,  and  therefore  the  scale,  over  which  the  index  actuated 
by  the  moving  needle  sweeps  will  be  graduated  in  divisions  of 
equal  width  for  equal  current  increments. 

The   original  form  of  this  type  of  mechanism  had  the   dis- 
advantage  that  when  the  current   strength  changed  abruptly 
the  index  did  not  show  the  new  value  at  once,  but  vibrated 
back  and  forth  on  its  scale  for  a  considerable  period.     This  can 
be  overcome  to  some  extent  by  making  the  moving  parts  ex- 
tremely   light,    in    order    to 
diminish  their  inertia,  and  by 
making    the    magnetic    field 
very    powerful,    which    of 
course    results    in    a   greater 
effort  to  prevent  the  needle 
from  swinging  past  the  point 
where  equilibrium  exists  be- 
tween the  directive  force  of 
the  magnet  and  that  of  the 
solenoid,  that  is  to  say  past 
the  line  whose  direction  is  the 
resultant  of  the  fields  due  to 
the    permanent   magnet   and 

the  current-carrying  coil.  A  greater  magnet  strength  means, 
however,  a  decreased  sensibility  and  increased  cost  of  structure, 
so  that  a  limit  in  this  direction  is  soon  reached.  The  damp- 
ing of  the  oscillations  that  would  still  exist  may  be  accom- 
plished, either  by  an  air  vane  moving  in  a  nearly  closed  box 
and  forming  an  air  dash  pot  or  by  an  oil  dash  pot.  It  may 
also  be  attained  magnetically  by  attaching  polar  extensions 
to  the  magnet,  as  shown  in  Fig.  117,  which  extensions  supply 
a  field  through  which  is  swept  a  short-circuited  conductor 
moving  with  the  movable  element.  Currents  are  set  up  in 
this  short-circuited  loop  when  the  needle  swings,  just  as 
in  the  case  of  a  short-circuited  armature  coil,  and  are  dissipated 
by  doing  the  work  necessary  to  overcome  the  loop's  resistance. 


FIG.  117. 


MEASUREMENT  OF  CURRENT. 


155 


The  energy  so  dissipated  is  subtracted  from  that  which  tends 
to  carry  the  moving  system  past  the  position  of  equilibrium,  and 
therefore  results  in  reducing  very  materially  the  number  of 
swings  and  the  time  to  obtain  a  reading. 

Another  commercial-indicating  instrument  suitable  for  direct 
current  measurements  only  and  containing  a  stationary  per- 
manent magnet  and  a  fixed  coil  of  wire,  is  one  made  by  the 
Whitney  Electrical  Instrument  Company. 

Referring  to  Fig.  118,  NS  is  a  U-shaped  permanent  mag- 
net, and  m  a  short  piece  of  soft  iron  secured  diagonally  to  the 

JLn 


•ytr-i 

t-7?                                                                     —  — 

|jr  :                                   ~\ 

1        A 

J 

& 

JU 

FIG.  118. 


shaft,  B,  and  rotating  with  it.  A  is  a  stationary  spool  contain- 
ing the  windings,  (7,  through  which  the  current  to  be  measured 
is  passed,  /  is  a  pointer  for  indicating  the  extent  of  rotation  of 
the  shaft,  and  D  is  a  spring  opposing  that  rotation.  The  iron 
piece,  sn,  is  evidently  polarized  by  the  stationary  magnet,  just 
as  is  the  needle  sn  in  the  Deprez-Carpentier  instrument,  Fig.  116, 
but  the  stationary  magnet  does  not  exert  any  effective  directive 
force  in  this  case,  as  whatever  the  position  that  sn  may  take  up 
by  the  rotation  of  the  shaft,  .5,  the  distance  between  its  ex- 
tremities and  the  inner  faces  of  the  magnet,  NS,  remains  the 


156       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

same,  and  hence  there  is  no  increased  or  decreased  effort  to  pull 
it  back.  When  current  flows  through  the  coil,  (7,  it  sets  up  a 
magnetic  flux  in  the  direction  of  the  dotted  arrow  shown  in  the 
plan  view  of  the  mechanism,  and  the  polarized  needle  of  course 
tends  to  take  up  a  position  parallel  thereto.  The  force  with 
which  the  needle  tends  to  rotate  is  in  proportion  to  the  current 
strength,  and  as  the  spring,  D,  supplies  an  opposing  force  in 
proportion  to  the  amount  that  it  is  wound  up  by  the  rotation  of 
the  shaft,  each  current  strength  has  a  corresponding  position  of 
equilibrium  of  the  needle,  J,  and  therefore  the  scale  under  / 
may  be  calibrated  directly  in  units  of  current  strength. 

These  instruments  are  damped  by  means  of  aluminum  vanes 
secured  to  the  shafts  and  swinging  between  the  jaws  of  a  small 
auxiliary  magnet.  Eddy  currents  are  set  up  in  such  a  vane 
when  it  moves,  and  these  check  the  swings  as  before  explained. 
The  form  is  considerably  more  sensitive  than  the  older  Deprez- 
Carpentier  ones. 

MOVING  COIL  INSTRUMENTS. 

If  the  d'  Arson  vial  galvanometer  mentioned  on  page  46  be 
graduated  by  comparison  with  some  standardized  current-meas- 
uring instrument,  it  may  be  and  often  is  used  as  a  milliammeter, 
or  millivoltmeter.  Such  apparatus  is,  however,  clumsy  and 
unnecessarily  sensitive,  and  the  use  of  a  beam  of  light  for 
taking  the  readings  is  rather  inconvenient.  In  instruments  of 
this  class  for  the  regular  measurement  of  commercial  current 
strengths  the  suspension  strips  of  the  reflecting  galvanometers 
are  replaced  by  pivots  working  in  jeweled  bearings,  and  a  needle 
attached  to  the  coil  is  moved  by  it  over  a  calibrated  scale, 
instead  of  the  mirror  and  light  beam  arrangement,  a  commercial- 
moving  coil  instrument,  thus  forming  the  same  modification  of 
the  d'Arsonval  galvanometer  that  the  Deprez-Carpentier  instru- 
ment forms  of  the  Thompson  galvanometer. 

A  common  form  of  this  d'Arsonval  type  of  ammeter,  built 
along  the  above  lines,  is  the  well-known  W.eston  instrument, 
whose  mechanism  is  shown  in  Fig.  119.  The  rotation  of  the 
active  coil  in  this  and  similar  meters  is  opposed  by  a  pair  of  flat 
spiral  springs  whose  inner  ends  are  electrically  connected  to  the 
coil  terminals,  and  whose  outer  ends  are  secured  to  fixed  abut- 
ments through  which  the  current  is  led  into  and  out  of  the 


MEASUREMENT  OF  CURRENT. 


157 


apparatus.  The  springs  offer  an  opposing  force  that  increases 
in  direct  proportion  to  the  angle  through  which  they  have  been 
wound  up,  and,  as  the  torque  increases  in  direct  proportion  to 
the  current  strength,  equal  current  increments  produce  equal 
increments  of  the  excursions  of  the  needle,  that  is  to  say,  the 
scale  is  equally  divided. 

In  this  instrument,  as  in  the  original  d' Arson val  form,  the 
tendency  of  the  coil  to  oscillate  about  the  point  of  equilibrium 
before  coming  to  rest  is  obviated  by  winding  the  moving  wire 
on  a  frame  of  metal  of  good  electrical  conductivity,  such  as 
copper  or  aluminum.  This  frame  acts  like  a  short>circuited 
conductor  in  a  motor  armature,  and,  as  stated  before,  consumes 
energy  which  is  subtracted  from  that  due  to  the  inertia  which 
tends  to  swing  the  needle 
beyond  the  position  of  equi- 
librium. 

The  strength  of  the  cur- 
rents that  can  be  passed 
through  the  winding  of  an 
instrument  of  this  descrip- 
tion is  very  small  as  com- 
pared with  those  used  in 
most  commercial  work,  as  the 
springs,  which  serve  also  as 
conductors,  become  over- 
heated and  lose  their  proper 
elasticity  if  a  very  small  cur-  FIG.  119. 

rent  flow  through  them  be  exceeded.  In  order  to  render  the 
apparatus  available  for  the  measurement  of  large  currents, 
the  same  expedient  is  used  as  that  employed  in  the  case  of 
reflecting  galvanometers  for  decreasing  their  sensibility,  and 
incidentally  increasing  the  amount  of  current  that  may  flow 
through  the-  galvanometer  circuit  without  injury,  that  is,  by 
using  a  shunt  and  diverting  the  major  portion  of  the  current 
through  that  by-path.  The  remarks  made  on  the  subject  of 
shunts  for  use  with  the  potentiometer  when  measuring  current 
strengths  (see  page  89)  also  apply  to  shunts  for  such  am- 
meters. 

An  ammeter  made  by  the  Whitney  Electrical  Instrument  Com- 
pany differs  from  the    conventional  d'Arsonval  form,  in  that, 


158       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

among  other  things,  there  is  only  one  gap  in  the  magnetic  circuit, 
instead  of  the  usual  two,  arid  that  the  coil  of  moving  wire  is  not 
symmetrical  to  the  axis  about  which  it  rotates. 

Fig.  120  illustrates  the  mechanism  of  this  type  of  instrument, 
the  outer  pole  piece  of  the  magnet  being  shown  as  transparent 
in  order  that  the  coil  arrangement  may  be  seen  more  clearly. 
As  in  the  case  of  the  Weston  meter,  the  indications  of  the 
Whitney  device  are  made  "  dead  beat "  by  winding  the  active- 
wire  on  a  spool  of  copper  or  aluminum,  the  currents  generated 
in  the  spool  tending  to  bring  it  rapidly  to  rest.  However,  the 
action  is  not  as  efficient  as  in  the  other  form,  because  in  order 
to  balance  the  moving  element  mechanically,  so  that  a  small  dif- 
ference in  the  angle  to  the  horizontal  at  which  the  meter  is  used 
will  not  introduce  an  appreciable  error,  a  counterweight  is  added 


FIG.  120. 

on  the  side  of  the  supporting  shaft  opposite  the  coil,  and  the  in- 
ertia of  this  carries  the  needle  slightly  beyond  the  position 
corresponding  to  the  new  current  strength,  when  that  current  is 
applied,  and  time  must  elapse  before  it  can  swing  back  again 
and  indicate  the  true  value.  On  the  other  hand,  the  construc- 
tion is  advantageous  in  affording  very  perfect  shielding  against 
disturbances  due  to  neighboring  magnetic  fields,  and  also  in 
that  it  allows  the  use  of  a  greater  clearance  between  the  coil 
and  pole  pieces. 

The  Kennelly  ammeter  is  shown  in  Fig.  121.  In  this  as 
in  the  Whitney  instrument  it  will  be  seen  that  there  is  but  a 
single  air  gap  in  the  magnetic  circuit ;  the  moving  conductors, 
however,  instead  of  being  wound  into  the  form  of  a  loop  are 
distributed  radially  on  a  flat  disk,  and  the  disk  itself  is  made  of 
a  good  conductor,  such  as  aluminum,  which  damps  the  swing 


MEASUREMENT  OF  CURRENT.  159 

of  the  indicating  needle,  not  as  in  the  case  of  the  two  preceding 
instruments,  by  setting  up  currents  as  in  a  short-circuited  turn 
of  motor  or  generator  armature,  but  by  the  eddy  currents  gene- 
rated. There  is  a  considerable  amount  of  inactive  wire  in  the 
moving  element  of  this  class  of  instrument,  because,  in  order  to 
avoid  leading  the  current  back  through  the  same  magnetic 
field,  which  would  render  it  inoperative,  the  turns  must  be 
carried  around  the  periphery  of  the  disk  for  a  considerable 
portion  of  its  circumference  before  they  can  again  be  led  back 
to  the  center  and  the  two  ends  connected  to  the  flat  spiral 


FIG.  121. 

springs,  to  which  electrical  connection  is  made  with  the  outside 
line,  and  which  exert  the  force  opposing  the  motion  of  the  disk. 
A  somewhat  similar  instrument  is  the  Thompson  ammeter, 
shown  in  Fig.  122.  In  this  as  in  the  Kennelly  meter  the 
moving  wire  is  mounted  on  a  flat  disk,  but  instead  of  having 
the  individual  conductors  follow  along  separate  radii,  they  are 
bunched  and  flow  along  a  single  diameter,  being  symmetrically 
divided  into  halves,  the  return  halves  of  each  portion  being  led 
along  opposite  semi-circumferences.  The  form  of  stationary 
magnet,  which  furnishes  the  magnetic  field  necessary  for  the 
operation  of  the  instrument,  is  also  different  from  that  in  the 
Kennelly  instrument.  There  are  two  of  these  magnets  placed 
with  their  poles  of  unlike  signs  adjacent.  While  the  necessity 
of  two  magnets  enhances  the  first  cost,  their  use  has  the  advan- 


160       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

tage  that,  if  the  instrument  be  placed  in  a  powerful  magnetic 
field,  whatever  additional  field  strength  is  caused  by  this  between 
the  poles  of  one  of  the  magnets  is  offset,  so  far  as  the  action  on 
the  movable  coil  is  concerned,  by  the  weakening  of  the  magnetic 
field  of  the  other  magnet.  In  other  words,  the  instrument  is 
astatic.  This  point,  however,  is  of  more  theoretical  than  prac- 
tical importance,  as  the  Whitney  form  is  practically  as  immune 
from  external  influences,  and  any  of  the  meters  described  may 
be  so  effectively  shielded,  for  commercial  purposes  at  least,  by 


FIG.  122. 

placing  them  within  an  iron  casing  that  no  further  protection 
is  needed. 

The  three  types  of  moving-coil  instrument  mechanisms  that 
have  been  briefly  mentioned  above  were  selected  in  order  to 
emphasize  what  has  been  mentioned  in  a  preceding  chapter, 
namely,  that  coil  instruments  for  the  commercial  measurement 
of  direct  current  are  nothing  more  or  less  than  special  electric 
motors,  in  which  the  field  magnet  is  stationary  as  usual  and  the 
armature  allowed  to  rotate  against  the  constantly  increasing 
resistance  of  a  spring  until  the  point  of  balance  is  reached. 


MEASUREMENT  OF  CURRENT. 


161 


J.,  Fig.  123,  makes  it  clear  that  the  original  d'Arsonval  form 
of  instrument,  as  exemplified  by  the  Weston  ammeter,  is  a  small 
motor  with  a  permanent  magnet  field,  having  a  stationary 
armature  core  and  a  section  of  armature  winding  of  the  con- 
ventional series  or  drum  wound  type  as  moving  element.  B  of 
the  same  figure  shows  that  the  Whitney  form  of  ammeter  is 
likewise  a  small  motor  with  a  permanent  magnet  field,  a  sta- 
tionary armature  core,  and  one  section  of  armature  coil  of  the 
Gramme  pattern  as  the  movable  element ;  whereas  the  cuts  O 
in  the  same  figure  show  that  the  Kennelly  and  Thompson  in- 


fl 


\  N         •Illllllll 

1)))'  ii(((t 

....      .         i  i       '     • 
^^ 


u 


B 


FIG.  123. 


struments  are  motors  having  armatures  of  the  radially  wound 
form.  In  each  case  the  opposing  force  may  be  that  furnished 
by  a  flat  spiral  spring  or  springs ;  gravitational  attraction  is 
sometimes  employed  when  the  apparatus  is  placed  in  a  favorable 
position,  or  magnetic  attraction  on  an  iron  needle  (see  page  52) 
may  be  used.  It  is  usual  to  conduct  the  current  to  and  from 
the  moving  coil  through  the  springs,  but  separate  flexible  con- 
ductors may  be  used  if  the  springs  be  absent,  or  if  it  is  desired 
to  electrically  reinforce  the  capacity  of  existing  springs. 

In  all  of  the  forms  it  is  impossible  to  pass  all  of  the  current  to 


162       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

be  measured  through  the  moving  coil  unless  the  current  be  of 
very  small  value,  and  recourse  is  had,  therefore,  to  shunts  for 
diverting  the  major  portion  of  the  current,  as  already  mentioned 
in  connection  with  galvanometers  in  Chapter  III. 

Shunted  ammeters  of  the  types  so  far  described  have  two 
great  advantages :  first,  their  scales  are  equally  divided,  which 
means  that  when  used  to  measure  the  output  of  constant 
potential  generators  or  the  load  on  such  circuits,  the  percentage 
of  full  load  being  carried  may  be  estimated  at  a  glance  from  the 
angular  position  of  the  pointer,  much  as  time  is  casually  read 
off  from  a  clock  from  the  relative  position  of  the  hands  without 
looking  at  the  numerals  on  the  dial.  Second,  and  more  impor- 
tant, the  amount  of  current  needed  by  the  instrument  itself 
to  produce  full  scale  deflection  is  so  very  small  that  it  is  easily 
carried  by  light  flexible  conductors,  the  shunt  leads,  with  the 
result  that  the  instrument  may  be  placed  in  any  convenient 
position,  irrespective  of  the  location  of  the  bus-bars,  the  shunt 
only,  carrying  the  predetermined  remaining  part  of  the  current, 
being  inserted  in  the  main  circuit. 

On  the  other  hand,  it  is  rarely  the  case  that  a  shunted  am- 
meter will  give  as  accurate  results  as  an  instrument  in  which 
the  whole  current  to  be  measured  is  passed  through  the  instru- 
ment windings.  First  of  all,  there  are  the  temperature  errors. 
In  order  that  the  windings  of  commercial  shunted  ammeters  may 
have  the  requisite  sensibility  they  are  of  necessity  composed 
largely  of  copper  wire,  a  material  whose  resistance  changes 
about  1  per  cent  for  every  5°  Fahr.  change  in  temperature. 
Therefore  if  the  shunt  is  of  a  material  having  a  practically  zero 
temperature  coefficient,  the  changes  in  resistance  of  the  instru- 
ment windings  become  important.  The  temperatures  at  which 
instruments  are  used  commonly  cover  a  range  of  from  40°  to  100° 
Fahr.,  which  if  the  calibration  were  effected  at  70°  Fahr.  means 
a  variable  error  of  6  per  cent,  which  cannot  properly  be  designated 
as  falling  within  allowable  limits.  If  the  shunt  be  made  of  copper 
so  that  its  resistance  increases  in  the  same  ratio  as  that  of  the 
instrument,  the  ratio  of  the  two  thus  remaining  the  same,  we 
encounter  the  fact  that  instruments  and  their  shunts  are  very 
seldom  of  the  same  temperature,  the  former  being  usually  on 
the  front  of  a  switchboard  where  the  temperature  may  be  taken, 
as  about  80  degrees  on  an  average,  and  the  latter,  in  the  rearsur- 


MEASUREMENT  OF  CURRENT.          163 

rounded  by  current-carrying  conductors,  rheostats,  and  the  like, 
often  boxed  in  so  as  to  be  at  a  temperature  of  120°  Fahr.,  or  more. 
This  would  mean  an  error  of  8  per  cent  if  the  instrument  and 
shunt  were  calibrated  at  the  same  temperature.  It  would  not 
be  safe  to  assume  that  the  shunt  will  always  be  at  a  point  where 
the  temperature  is  higher  than  that  at  which  the  instrument 
is  located,  either,  as  it  is  not  uncommon  to  find  switchboards 
erected  in  galleries  where  their  rears,  and  hence  the  shunts 
mounted  thereon,  are  exposed  to  direct  blasts  from  open  win- 
dows in  winter,  their  fronts,  where  the  instruments  themselves 
are  located,  being  at  the  same  time  subjected  to  the  hot  air  of 
the  interior  of  the  station.  The  compromise  that  leads  to  the 
minimum  value  of  the  greatest  error  possible  under  these 
varying  conditions  is  to  make  the  shunt  of  a  material  having 
a  temperature  coefficient  one  half  of  that  of  the  instrument 
circuit  formed  by  the  instrument  windings  with  the  attached 
flexible  leads.  The  error  is  in  this  way  halved,  but  even  then 
we  have  possible  variations  of  3  or  4  per  cent  from  the 
normal  from  this  one  cause  alone,  a  figure  which,  while  it 
would  have  no  earthly  effect  on  the  operation  of  99  per 
cent  of  the  plants  in  existence,  would,  if  known,  be  protested 
against  in  holy  horror  by  the  majority  of  the  operators  who  have 
heard  tales  of  accuracies  of  one  half  or  even  one  fifth  of  a  per 
cent  for  so  long  that  they  actually  expect  to  be  able  to  count 
on  this  being  attained  in  ordinary  practice. 

Another  very  common  source  of  error  in  shunted  ammeters  is 
the  resistance  at  the  point  of  contact  where  the  shunt  leads  are 
attached  to  the  instrument  and  the  shunt.  For  convenience  in 
constructing  the  switchboard  the  leads  are  usually  made  de- 
tached from  both  instrument  and  shunt,  and  the  connections 
are  finally  completed  by  securing  the  lead  ends  under  screw 
heads  and  washers  at  each  end,  making  a  total  of  four  of  such 
joints.  Now,  metallic  surfaces  become  corroded  and  screws 
often  work  loose  where  there  is  vibration,  with  the  result  that 
such  joints  become  of  very  uncertain  resistance  and  the  instru- 
ment readings  are  correspondingly  thrown  out.  Cases  have 
frequently  come  to  the  notice  of  the  author  in  which  brighten- 
ing the  surfaces  and  retightening  the  screws  has  caused  a 
difference  of  »25  per  cent  or  more  in  the  indications  with  the 
same  load.  Such  errors  can  obviously  be  minimized  by  careful 


164       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

periodic  inspection  of  the  contacts,  and  where  such  instruments 
are  installed  this  practice  should  be  faithfully  followed. 

The  error  pointed  out  on  page  89,  due  to  leading  the  current 
into  and  out  of  the  shunt  at  a  different  set  of  points  than  those 
used  when  calibration  was  effected,  seldom  enters  as  a  con- 
siderable factor  with  well-built  switchboards,  but  the  errors 
due  to  thermo  E.M.F.'s,  mentioned  on  page  90,  may  be  larger 
than  good  practice  will  permit.  One  manufacturer  avoids  the 
difficulty  by  the  expedient  mentioned  on  the-  page  referred  to, 
that  is  to  say,  by  placing  the  points  of  attachment  of  the  shunt 
leads  inside  of  the  distribution  terminals  of  the  shunt. 
Another  uses  the  following  special  plan : 
Referring  to  Fig.  124,  A  and  B  are  the  shunt  terminals,  D 
the  resistance  strip,  made  of  a  different  metal  from  the  terminals, 
E,  a  conductor,  of  the  same  material  as  D  and  C,  a  terminal  of 
the  same  material  as  A,  secured  to  A  in  such  a  manner  tkat  the 
thermal  contact  is  good,  but  the  two  are  electrically  insulated. 

If,  now,  the  block 
B  is  at  a  higher 
temperature  than 
the  block  A,  due, 
for  instance,  to  a 
poorer  contact  be- 

124.  tween  B  and  its 

bus-bar,  there  will 
be  a  lesser  thermo  electric  E.M.F.  at  the  junction  between 
A  and  D  than  at  the  junction  between  .B  and  D,  and  if  the 
values  of  these  E.M.F.'s  are  1  millivolt  and  2  millivolts  re- 
spectively, there  would  be  a  difference  of  potential  of  1  milli- 
volt between  A  and  J9,  due  to  that  cause  alone  which  would 
be  added  to  or  subtracted  from  that  due  to  the  drop  in 
potential  across  the  shunt  terminals  because  of  the  current 
flowing  through  it,  and  would  hence  introduce  a  corresponding 
error  in  the  indications  of  the  instrument  if  the  leads  were 
attached  at  these  points.  If,  however,  one  instrument  lead  is 
attached  to  J.,  and  the  other  to  (7,  as  shown  in  the  figure,  the 
equal  and  opposing  E.M.F.'s  at  the  junctions  between  A  and  D 
and  C  and  E  cancel  one  another,  and  the  E.M.F.  between  A 
and  (7,  being  then  that  due  to  the  drop  of  potential  because  of 
the  current  flowing  only,  thus  becomes  in  direct  proportion  to 


MEASUREMENT  OF  CURRENT. 


165 


FIG.  125. 


the  current  strength.     A  shunt  of  this   kind  is  illustrated  in 
Fig.  125. 

AMMETERS  FOR  BOTH  DIRECT  AND  ALTERNATING  CURRENT. 
THE  KELVIN  AMPERE  BALANCE. 

As  was  pointed  out  in  the  chapter  on  laboratory  standards 
for  the  measurement  of  current,  the  Kelvin  ampere  balance 
works  equally  well,  whether 
the  current  be  direct  or 
alternating,  as,  in  the  latter 
event,  the  current  in  the  ^ 
various  coils  reverses  simul- 
taneously and  the  resultant 
effort  is  always  to  urge 
one  end  of  the  balance  up  and  the  other  down. 

This  instrument,  however,  hardly  belongs  in  the  class  of 
apparatus  for  the  commercial  measurement  of  current  strengths 
as  its  bulk,  weight,  and  cost,  the  length  of  time  required  to 
obtain  a  reading,  and  the  fact  that  it  is  not  direct  reading, 

render  it  unsuited  for  all  except 

laboratory  work. 

SIEMENS.'    DYNAMOMETER. 

This  familiar  instrument,  illus- 
trated in  Fig.  126,  consists  of 
two  conductors,  each  wound  into 
coil  form,  one  of  them  being  sta- 
tionary and  surrounded  by  the 
other,  their  axes  being  in  line, 
but  their  planes  at  right  angles. 
The  outer  coil  is  suspended  by 
a/fine  silken  fiber  or  a  steel  pivot 
resting  on  a  jewel  bearing,  and 
has  secured  to  its  upper  side  one 
end  of  a  spiral  spring  whose  otiier 
extremity  is  made  fast  to  what 
is  called  a  "  torsion  head."  This  torsion  head  is  a  button 
which  can  be  manually  rotated  about  its  axis  and  which  carries 


FIG.  126. 


166      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

a  pointer  that  sweeps  over  a  scale  divided  into  degrees. 
Attached  to  the  outer  coil  itself  there  is  another  pointer  coming 
up  to  the  same  scale,  but  whose  motion  is  limited  by  two  closely 
adjacent  stops.  Current  is  conducted  to  and  from  the  outer 
coil,  through  mercury  cups  secured  to  the  frame  of  the  appa- 
ratus, and  the  electrical  connections  between  the  two  coils  are 
usually  so  made  that  the  current  to  be  measured  has  to  flow 
first  through  one  and  then  through  the  other,  they  being  con- 
nected in  series.  When  current  flows  in  this  way,  the  suspended 
coil  tends  to  turn  so  that  its  plane  is  parallel  to  that  of  the 
stationary  coil,  something  that  is  not  possible  because  of  the 
stops  which  limit  the  play  of  the  so-called  zero  needle  attached 
to  it.  To  bring  the  zero  needle  back  to  the  position  from  which 
it  started,  and  which  is  generally  called  the  zero  mark,  the 
knurled  button  secured  to .  the  spring  is  rotated  until  coinci- 
dence is  shown.  The  torsion  spring  is  now  subject  to  a  stress 
which  is  equal  to  the  reaction  between  the  fixed  and  moving 
coils,  and  the  amount  of  the  said  stress,  as  indicated  by  the 
pointer  attached  to  the  torsion  head  and  showing  the  amount 
that  the  spring  has  been  wound  up,  gives  the  current  strength, 
as  each  apparatus  is  provided  with  a  set  of  curve  sheets,  from 
which  the  ampere  value  corresponding  to  any  scale  degree  may 
be  read  off. 

The  Siemens  instrument  can  be  made  more  permanent,  so 
far  as  its  accuracy  is  concerned,  than  the  direct  current  devices 
before  described,  as  the  uncertain  element  of  the  strength  of  the 
permanent  magnet  entering  into  the  construction  of  the  D.C. 
instruments  is  eliminated  and,  as  the  single  spring  does  not 
carry  current,  there  is  no  danger  of  having  its  elasticity  modi- 
fied by  being  overheated  from  that  cause.  On  the  other  hand, 
the  mercury  contacts  are  a  nuisance,  as  the  cups  must  be 
drained  before  the  instrument  can  be  transported,  and  the  con- 
stant reference  from  scale  reading  to  curve  and  back  to  note- 
book is  very  trying,  when  numerous  observations  are  to  be 
made.  They  also  share  the  same  objection  to  which  a  large 
majority  of  alternating  current  instruments  are  open,  that  is, 
that  the  field  furnished  by  the  stationary  coil  is  but  weak,  and 
neighboring  fields  may  form  a  considerable  percentage  thereof. 
This  makes  no  difference  when  alternating  currents  are  being 
measured,  as  what  the  foreign  field  adds  to  the  instrument  coil 


MEASUREMENT  OF  CURRENT.         167 

field  when  current  flows  in  one  direction,  is  subtracted  when 
the  current  flow  reverses.  When  measuring  direct  current, 
however,  this  favorable  condition  does  not  exist,  and  if  accurate 
results  are  to  be  had,  it  is  necessary  to  pass  the  current  through 
the  instrument  first  in  one  direction,  noting  results,  and  then, 
with  the  minimum  possible  delay,  reversing  the  connections  and 
noting  the  new  result.  The 
true  value  may  safely  be  taken 
as  the  arithmetical  mean, 
namely,  one  half  the  sum  of  the 
two  observations. 

ELECTROMAGNETIC    INSTRU- 
MENTS. 

Kohlrausch  Instruments. 
One  of  the  earliest,  if  not  the 
earliest,  form  of  electrical  meas- 
uring instruments  is  that  in 
which  the  current  to  be  meas- 
ured is  passed  through  a  hollow 
coil  of  wire,  that  is,  a  solenoid, 
and  its  force  measured  by  the 
attraction  exerted  on  a  mag- 
netic body  suspended  within 
the  core.  The  simplest  ex- 
ample of  such  an  instrument  is 
the  Kohlrausch,  shown  in  Fig. 
127.  The  solenoid  in  this  in- 
strument surrounds  a  long  thin 
iron  wire  which  is  suspended 
from  above  by  a  coiled  spring 
similar  to  that  in  the  ordi- 
nary spring  balance.  A  pointer  FlG- 127' 
secured  to  the  iron  wire,  or  a  prolongation  thereof,  moves  ver- 
tically over  a  scale,  empirically  graduated  to  show  current 
strengths.  Such  an  instrument  will  work,  whether  the  current 
flowing  through  the  solenoid  be  direct  or  alternating,  but  care 
must  be  used  in  the  design  if  accurate  results  are  to  be  at- 
tained when  the  instrument  is  used  with  both  kinds  of  current, 
because  if  the  iron  be  hard,  or  of  too  large  a  mass,  the  indica- 


168      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

tions  will  not  be  correct  for  both,  unless  separate  scales  be 
drawn.  For  ammeters,  the  best  design  calls  for  the  use  of  a 
very  fine  iron  wire  for  the  moving  element,  as  this  eliminates 
to  a  great  degree  the  error  due  to  varying  frequencies,  and  also 
has  the  advantage  of  making  the  scale  of  more  convenient 
divisions.  The  latter  holds  good,  because  of  the  fact  that  the 
attraction  of  a  solenoid  on  an  iron  core  varies  as  the  square  of 
the  strength  of  the  current  until  the  core  is  magnetically  sat- 
urated, after  which  time  the  attraction  becomes  directly  propor- 
tionate to  the  current  strength.  With  a  very  small  core,  there- 
fore, the  part  of  the  scale  in  which  the 
divisions  are  of  unequal  width  is  a 
very  small  one,  in  fact,  it  is  possible 
so  to  design  the  apparatus  that,  from 
10  per  cent  of  full  capacity  upward, 
the  scale  divisions  will  be  practically 
equally  spaced  for  equal  current  in- 
crements. 

In  voltmeters,  the  iron  core  is  usu- 
ally made  more  massive,  in  order  that 
the  law  of  squares  may  hold  good 
throughout  a  good  part  of  the  range, 
as  this  gives  more  open  divisions  at 
the  part  of  the  scale  where  readings 
are  usually  taken. 

Atkinson  Instrument. 

The  Kohlrausch  electromagnetic  in- 
struments are  not  in  common  use  in 
this  country,  but  find  their  greatest 
popularity  on  the  continent  of  Europe. 
In  England  a  modification  thereof  is  used  to  a  limited  extent. 
The  instrument  referred  to  is  the  "Atkinson,"  diagrammati- 
cally  illustrated  in  Fig.  128.  In  this  the  solenoid  surrounds  a 
vessel  containing  a  fluid  in  which  floats  a  sealed  hollow  glass 
cylinder  with  a  graduated  stem,  very  similar  to  a  hydrometer. 
The  iron  wire  is  placed  inside  of  this  float,  so  that  the  pull 
exerted  by  the  current  flowing  through  the  solenoid  is  against 
the  buoyant  effect  of  the  liquid  on  the  more  or  less  submerged 
float,  instead  of  a  coiled  spring.  This  modified  Kohlrausch 


FIG.  128 


MEASUREMENT  OF  CURRENT. 


169 


instrument  gives  indications  that  are  much  more  "dead  beat" 
than  those  of  the  original  form,  but  this  is  at  the  expense  of 
simplicity  and  portability. 

One  of  the  best,  and  to-day  most  widely  used  forms  of  elec- 
tromagnetic ammeters,  retains  the  feature  of  a  very  fine  iron 
wire  suspended  in  the  center  of  a  current  carrying  solenoid,  but 
instead  of  having  the  extent  of  motion  of  this  wire  indicate 
directly  the  current  values,  the  motion  is  first  translated  into 
that  of  a  pivoted  pointer  that  swings  over  a  graduated  circle 
arc. 

Fig.  129  shows  the  construction  of  such  an  instrument.  The 
iron  wire  is  suspended  from  an  arm  rigidly  secured  to  an  axle 


Counterbalance  far  Needle. 


Weight  W 


FIG.  129. 

whose  ends  are  pointed  and  rest  in  jewel  bearings,  and  the 
same  axle  carries  a  pointer  and  a  weight,  W,  which,  as  the 
needle  moves,  offers  an  increased  resistance  to  its  displacement. 
The  figure  is  so  nearly  self-explanatory  that  it  is  needless  to  go 
into  the  construction  at  further  length. 

If  the  swings  of  the  needle  of  electromagnetic  instruments 
like  this  be  damped,  either  by  a  suitable  air  vane  moving  in  a 
nearly  closed  box,  or  by  a  piston  fitting  very  loosely  in  an  open 
ended  cylinder  nearly  filled  with  viscous  oil,  we  have  a  form 
of  apparatus  that  is  exceptionally  well  suited  for  use  on  a 
switchboard  of  an  industrial  plant.  The  accuracy  can  be  made 
more  than  sufficient  for  commercial  purposes,  by  proper  design 
and  careful  selection  of  the  iron  ;  moreover,  there  are  no  parts 


170      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


liable  to  change  through  age,  the  force  opposing  the  needle's 
swing  being  that  due  to  gravitational  attraction,  and  there  being 
no  springs  or  permanent  magnets.  Furthermore,  the  apparatus 
is  available  for  either  direct  or  alternating  current. 

Kelvin  Ampere  Granges. 

Lord  Kelvin,  one  of  our  foremost  authorities  on  matters  per- 
taining to  electrical  measurements  and  electrical  measuring 
apparatus,  has,  within  the  last  few  years,  put  the  seal  of  his 

approval  on  instruments  of 
this  class,  by  redesigning  and 
putting  on  the  market,  under 
his  name,  the  Kelvin  ampere 
gauges,  one  of  ^hich  is 
shown  in  Fig.  130.  As  may 
be  seen  from  this  illustration, 
the  dead  beating  is  effected 
by  an  oil  damper,  the  mova- 
ble element  is  supported  on 
hooks  which  allow  of  a  rol- 
ling motion,  and  the  opposing 
force  is  that  of  gravity.  The 
extreme  reliability  of  these 
instruments  has  led  to  their 
wide  adoption  abroad,  and 
the  author  expects  to  see 
similar  types  extensively 
used  in  this  country  before 
the  lapse  of  many  years.  The 
station  engineer  will  be  far 

better  satisfied  with  an  ammeter  that  is  accurate  to  only  one 
or  one  and  a  half  per  cent,  when  installed,  but  which  will  retain 
that  accuracy  unchanged  for  an  indefinite  period,  than  with  a 
meter  of  a  questionable  quarter  or  half  per  cent  error  on 
erection,  that  may  become  an  unknown  amount  greater  in  the 
course  of  a  few  months,  because  of  magnet  or  spring  strength 
changes,  varying  lead  resistances,  etc.  The  accuracy  of  a 
solenoid  ammeter  is,  moreover,  for  all  practical  purposes,  abso- 
lutely independent  of  temperature,  whereas  shunted  ammeters 


FIG.  130. 


MEASUREMENT   OF   CURRENT.  171 

may,  as  before  explained,  have  temperature  errors  that  may  be 
as  great  as  1  per  cent  for  a  change  of  5  degrees. 

In  large  capacities,  solenoid  ammeters  are  not  inexpensive, 
as  the  construction  of  a  coil,  even  of  but  one  or  two  turns,  to 
carry  heavy  currents  is  a  costly  mat- 
ter. They  are,  also,  expensive  to 
install,  as  it  is,  of  course,  necessary 
to  pass  the  entire  current  to  be  meas- 
ured through  the  meter,  and  this 
means  extensions  and  complicated 
rearrangements  of  heavy  copper  bus- 
bars. 

To  meet  this  last  objection,  Lord 
Kelvin  places  the  solenoid  with  its 
accompanying  core  on  the  bus  bars 
themselves,  and  runs  a  light  cord 
from  the  core  to  an  arm  actuating 
the  swinging  needle,  enclosed  in  a  FlG  131 

conventional  case  and  swinging  over 

the  usual'  graduated  scale.  In  such  case  it  is  necessary  that 
the  indicating  portion  of  the  instrument  be  located  vertically 
above  the  actuating  part,  but  the  indicating  portion  is  still  free 
to  assume  any  form,  usually  either  the  type  shown  in  Fig.  130, 
or  the  so-called  edgewise  type,  shown  in  Fig.  131. 

Thomson  Inclined  Coil  Instruments. 

The   Thomson  inclined  coil  ammeter  is  an  electromagnetic 
instrument  extensively  used  in  this  country  for  the  measure- 


FlG.  132. 


ment  of  relatively  small  currents.     In  it,  as  will  be  seen  from 
Fig.  132,  the  stationary  coil  of  wire  is  placed  at  an  angle  to  the 


172      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

axis  of  the  staff  of  the  indicating  needle  and  the  staff  carries  a 
strip,  or  bundle  of  strips,  of  iron,  which,  when  no  current  is 
passing,  are  held  so  that  their  plane  is  nearly  parallel  to  the 
plane  of  the  coil.  When  current  is  put  on,  the  bundle  of  strips, 
of  course,  tends  to  take  up  a  position  such  that  the  reluctance 
of  the  magnetic  circuit  of  the  solenoid  is  reduced  to  a  mini- 
mum, and  in  so  doing,  of  necessity  rotates  the  iron  and  with  it 
the  shaft  to  the  position  shown  by  the  dotted  line.  The  force 
with  which  it  tends  to  rotate  is  in  proportion  to  the  current 
strength,  so  that  the  amount  that  it  winds  up  the  volute  phos- 
phor bronze  spring  which  opposes  its  motion,  as  indicated  by  the 
attached  needle,  indicates  the  current  strength.  The  arrange- 
ment of  parts  in  this  instrument  results  in  a  large  angular 
motion  of  the  needle,  without  necessitating  the  use  of  any 


FIG.  133. 

multiplying  devices,  such  as  levers,  gears,  or  pulleys.  When 
properly  designed  and  built,  this  instrument  is  capable  of  a 
very  satisfactory  degree  of  accuracy  and  reliability. 

Magnetic   Vane  Instruments. 

Another  form  of  electromagnetic  ammeter,  called  the  "  mag- 
netic vane  type,"  and  in  extensive  use  in  this  country,  is  dia- 
grammatically  shown  in  Fig.  133.  Here  the  current  passes 
through  a  solenoid,  whose  axis  is  at  right  angles  to  the  face  of 
the  instrument. 

Permanently  secured  inside  of  the  solenoid  spool  is  a  strip  of 
soft  iron  which  when  unrolled  is  triangular  in  shape,  the  base 


MEASUREMENT  OF  CURRENT.  173 

of  the  triangle  being  bent  out  at  right  angles,  as  the  figure 
shows.  Also  within  the  solenoid  core  is  a  steel  staff  or  shaft 
whose  pointed  ends  rest  in  appropriate  jewel  bearings,  and 
which  carries,  in  addition  to  the  indicating  needle,  a  flat  rect- 
angular strip  of  soft  iron,  which  is  parallel  to  the  bent  in 
stationary  piece  when  no  current  is  on. 

When  current  passes  through  the  wire  coil,  the  stationary  and 
movable  strips  are,  of  course,  similarly  magnetized,  so  that  the 
like  poles  of  the  magnets  so  formed  are  adjacent ;  they  there- 
fore repel  each  other,  and  in  so  doing  the  movable  one  carries 
with  it  over  the  scale  the  indicating  needle. 

This  form  of  instrument  has  many  modifications,  differing  in 
more  or  less  important  details.  The  force  opposing  the  motion 
of  the  needle  is  sometimes  that  offered  by  a  flat  spiral  spring, 
and  sometimes  the  attraction  of  gravity  on  a  weighted  arm. 
Like  other  electromagnetic  instruments,  this  type  is  operative 
with  either  direct  or  alternating  current,  and  its  motions  are 
damped,  preferably,  by  means  of  the  air  vane  or  the  oil  dash  pot. 

Electromagnetic  instruments  in  which  a  portion  of  the  iron 
used  is  stationary,  are  open  to  certain  objections,  experiment 
showing  that  there  are  errors,  when  a  fixed  plate  of  magnetic 
material  is  present,  that  exist  to  a  much  less  extent  when  such  a 
plate  is  not  used.  This  error  is  mainly  due  to  the  following  cause : 
Referring  to  the  chapter  on  magnetic  hysteresis  (see  page  380), 
the  flux  through  a  magnetic  circuit,  composed  wholly  of  iron, 
has  different  values  for  the  same  magnetizing  force,  according 
to  whether  the  magnetizing  force  be  increasing  or  decreasing. 

When,  on  the  other  hand,  the  iron  is  removed,  the  flux  is  the 
same,  no  matter  how  any  given  current  value  has  been  reached, 
that  is  to  say,  air  is  non-hysteretic.  In  a  composite  magnetic 
circuit,  formed  partly  of  air  and  partly  of  iron,  such  as  that  in 
the  instruments  in  question,  the  hysteretic  influence  of  the  iron 
decreases  as  the  percentage  of  the  total  magnetic  circuit  formed 
by  the  iron  decreases.  In  the  magnetic  vane  type  of  instrument, 
therefore,  involving  stationary  as  well  as  movable  iron,  the 
error  due  to  hysteresis  is  thus  increased,  so  that  there  is  a  greater 
discrepancy  between  the  values  of  a  rising  and  falling  current 
of  the  same  strength. 

The  character  of  the  iron  entering  into  the  construction  of  all 


174       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

electromagnetic  instruments  is  of  great  importance,  as  the 
hysteresis  losses  vary  widely  in  different  specimens  of  the 
metal.  While  careful  design  and  a  proper  selection  of 
the  iron  may  result  in  an  instrument  in  which  the  difference 
in  indications  between  a  rising  and  falling  current  of  the  same 
strength  is  no  greater  than  one  half  of  one  per  cent,  poor  design 
and  poor  iron  may  cause  an  error  of  5  per  cent,  or  over.  It 
is  advisable,  therefore,  carefully  to  test  electromagnetic  instru- 
ments intended  for  use  in  direct  current  work,  before  assuming 
that  they  are  correct  and,  moreover,  to  repeat  the  checking  at 
intervals,  because  iron  ages  magnetically,  and  has  a  higher 
hysteretic  coefficient,  after  being  subject  to  changes  in  the 
intensity  of  its  magnetization  for  extended  periods.  The  effect 
of  aging  is  negligible  in  some  brands  of  iron,  and  can  be  reduced 
in  all  by  proper  preliminary  treatment,  although  this  fact  does 
not  seem  to  be  appreciated  by  all  instrument  makers.  '\Vhere 
electromagnetic  instruments  are  used  for  the  measurement  of 
alternating  currents,  the  first  source  of  error,  namely,  the  dif- 
ference in  indications  between  a  rising  and  a  falling  current, 
does  not  exist,  by  reason  of  the  continuous,  automatic  reversal 
that  is  going  on  and  which  was  present  when  calibration  was 
effected. 

HOT    WIRE    INSTRUMENTS. 

When  an  electric  current  flows  through  a  conductor,  the 
energy  expended  in  overcoming  the  conductor's  resistance  is 
manifested  in  the  form  of  heat.  The  energy  consumed  varies 
as  the  square  of  the  current  strength,  and  the  temperature 
varies  proportionately,  so  that,  as  a  body  brought  to  different 
temperatures  expands  and  contracts,  these  variations,  suitably 
indicated,  may  be  utilized  as  a  means  of  measuring  current 
strengths. 

The  amount  of  elongation  of  a  heated  conductor  depends  on 
the  temperature  rise,  the  length  of  the  rod  or  wire,  and  the 
material  of  which  it  is  composed. 

Cardew  Instruments. 

In  what  is,  perhaps,  the  earliest  commercial  form  of  hot  wire 
instrument,  namely,  the  Cardew,  the  conductor  is  a  platinum 
silver  wire,  about  seven  feet  in  length,  arranged  as  shown  in 


MEASUREMENT    OF    CURRENT. 


175 


Fig.  135.  It  is  coiled  back  and  forth  over  ivory  pulleys  in 
order  to  decrease  the  length  of  the  instrument,  and  the  motion 
is  amplified  by  a  gear  wheel  and  segment,  or  a 
pulley  and  cord,  so  that  the  needle  traverses 
an  arc  of  over  three  hundred  degrees.  To 
prevent  air  currents  from  cooling  the  wire,  the 
whole  is  enclosed  in  a  case,  the  wire  and  lower 
pulleys  being  shielded  by  a  brass  tube.  As  the 
coefficient  of  expansion  of  the  brass  tube  and 
the  platinum  silver  wire  are  not  identical,  it  is 
evidently  not  feasible  to  attach  the  bearings  for 
the  pulleys  over  which  the  wire  passes,  to  the 
tube,  for,  if  this  were  done  and  the  instrument 
placed  where  the  temperature  was  not  that  which 
existed  at  the  time  when  the  instrument  was 
calibrated,  the  difference  between  the  expansion 
of  the  tube  and  that  of  the  wire  would  cause 
the  needle  to  move.  The  pulleys  are,  there- 
fore, mounted  on  a  framework  built  up  on  a  com- 
bination of  brass  and  iron  rods,  with  the  lengths 
of  these  respective  metals  so  selected  that  the 
whole  expands  and  contracts  with  changes  of 
temperature  at  the  same  rate  as  the  platinum 
silver  wire.  Fig.  136  shows  the  complete  meter. 

The  Cardew  instrument  should  not  be  used 
with  the  tube  in  a  vertical  position  as  air  cur- 
rents are  then  set  up  within  it  by  the  heated  wire, 
and  the  cooling  effect  of  these  currents  on  other 
portions  of  the  wire  causes  an  appreciable  error. 
The  tube  is,  therefore,  always  placed  horizon- 
tally, when  possible. 

While  abundantly  able  to  satisfy  the  require- 
ments existing  when  it  was  devised,  the  Cardew 
instrument,  as  just  described,  does  not  compare 
favorably  with  modern  hot  wire  types.  The 
errors  introduced  by  the  friction  of  the  bearings 
of  the  numerous  wheels  it  contains,  the  disturb-  FlGt  135* 

ing  effect  of  air  currents  set  up  in  the  tube  by  the  heated  wires, 
and  the  generally  unsatisfactory  result  of  leading  a  wire  around 
the  sharp  bend  of  a  pulley  when  the  expansion  of  its  whole 


176       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

length  is  to  be  utilized,  render  its  indications  too  inaccurate 
for  present  day  demands.  The  electromagnetic  and  moving  coil 
instruments  that  have  been  developed  since  its  time  are  much 
better  and,  because  but  little  work  was  done  on  apparatus  util- 
izing the  hot  wire  principle  for  a  considerable  period,  the  preva- 
lence of  these  other  forms  has  led  many  to  believe  that  the 
principle  itself  is  inherently  defective.  Such,  however,  is  not 
the  case,  as  hot  wire  measuring  instruments  when  properly 
designed,  are  capable  of  making  a  showing  that  is  fully  satisfac- 
tory as  compared  with  that  of  the  other  types. 

Hartmann  and  Braun  Instruments. 

Not  only  is  the  length  of  the  Cardew  instrument  objection- 
able, but  the  wire  therein  must  be  run  at  such  high  tempera- 
tures, in  order  to  obtain  a  sufficient  linear  expan- 
sion to  work  the  indicating  gear,  that  the  amount 
of  energy  consumed  renders  its  use  impossible  for 
the  measurement  of  small  currents  when  the  allow- 
able drop  in  E.M.F.  in  the  meter  is  small,  or  for 
very  large  currents  where  the  potential  necessary 
to  force  the  current  through  the  instrument  is  ob- 
tained from  the  drop  across  the  terminals  of  a 
resistance  placed  in  the  main  circuit,  that  is,  it 
cannot  be  used  as  a  shunt  ammeter.  The  Hartmann 
and  Braun  hot  wire  instruments  overcome  these 
disadvantages,  to  a  considerable  degree,  by  the  em- 
ployment of  a  somewhat  different  principle.  It  is 
well  known  that,  if  a  wire  strand  be  stretched  be- 
tween two  fixed  points,  the  amount  that  it  will 
sag  at  its  center,  when  the  strand  is  slightly 
stretched,  is  many  times  the  elongation  of  the 
strand  itself.  Referring:  to  Fig:.  137,  AS  is  the 

FIG.  136.  ...       ,,       &TT 

expansion  wire  in  the  Hartmann  and  Braun  in- 
strument, which,  when  current  flows  through  it,  stretches  and 
allows  its  center  to  sag.  At  the  center  is  attached  one  end  of 
a  wire,  CD,  secured  to  a  fixed  point  at  D.  When  the  distance 
between  O  and  D  lessens,  because  of  the  sag  of  the  hot  wire,  CD 
is  itself  pulled  aside  by  the  spring  attached  to  its  center,  by  an 
amount  that  is  as  much  greater  than  the  sag  of  AB,  as  the  sag 


MEASUREMENT  OF  CURRENT. 


177 


of  AB  is  greater  than  the  elongation  of  A  B.  At  the  point,  E, 
in  the  center  of  CD,  there  is  attached  a  cord,  6r,  which  passes 
around  a  pulley  fastened  on  an  axis  carrying  an  indicating 
needle,  and  this  cord  is  kept  taut  by  the  spring,  8.  In  this  way 
a  very  short  hot  wire  elongates  sufficiently  with  a  reasonable  rise 
in  temperature  to  cause  readily  readable  needle  deflections. 
The  terminals  of  the  hot  wire  are  attached  to  a  common  metallic 
framework,  but  are  electrically  insulated  therefrom.  The  metal 
of  the  framework  has  the  same  coefficient  of  expansion  as  the 
wire,  so  that  changes  in  the  temperature  of  the  surround- 
ing atmosphere  affect  both  equally,  and  do  not  give  rise  to 
erroneous  indications.  It  is  claimed  that  with  a  voltage  as  low 
as  300  millivolts  at  the  terminals  of  conductors  attached  to  A 

n  B 


tfH-^/wvw-^ 
s 


E 


rJ> 


FIG.  137. 


and  B,  sufficient  current  will  flow  through  the  wire  to  cause  it 
to  expand  to  an  amount  that  will  make  the  indicating  needle 
traverse  full  scale.  This  drop  is  one  that  is  readily  attainable 
with  a  shunt  whose  size  and  cost  are  not  prohibitive,  and  which 
does  not  call  for  an  unreasonable  drain  of  energy  from  the  circuit. 
The  end  A  of  the  expansion  wire  is  secured  to  a  special 
terminal  part  as  shown.  This  is  provided  in  order  that  the  zero 
position  of  the  needle  may  be  adjusted  by  varying  the  tension 
of  AB,  should  this  at  any  time  be  necessary.  A  complete 
Hartmann  and  Braun  hot  wire  type  instrument  of  the  kind 
made  in  this  country  is  shown  in  Fig.  138.  The  device 
having  the  shape  of  a  wheel  with  opposite  segments  indented, 
attached  to  the  axis  of  the  pointer,  is  of  thin  sheet  aluminum, 
and  moves  between  the  pole  faces  of  the  permanent  magnet, 


178      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

the  eddy  currents  set  up  in  the  aluminum  when  the  needle 
swings  assisting  in  bringing  it  rapidly  to  rest  and  making 
the  indications  dead  beat. 

Roller  Hot  Wire  Instruments. 

The  principle  on  which  these  instruments  operate  is  dia- 
gram matically  shown  in  Fig.  139.  Referring  to  it,  a  wire,  a£, 
of  high  resistance,  low  temperature  coefficient  and  non-oxidiz- 
able  metal  is  secured  at  one  end  to  a  plate,  c^  passed  around  a 
pulley,  d,  secured  to  a  shaft,  e,  and  its  free  end  brought  back 
again  and  mechanically,  though  not  electrically,  attached  to  the 
same  plate,  c.  Plate,  <?,  is  kept  under  stress  by  the  spring,  /, 
which  constantly  tends  to  pull  it  in  a  direction  at  right  angles 


FIG.  138. 

with  the  axis  of  the  shaft,  e,  and  is  so  guided  that  it  can  move  in 
that  one  direction  only.  To  the  shaft,  e,  is  likewise  secured  an 
arm,  g,  bifurcated  at  one  end  and  counterweigh  ted  at  the  other. 
Between  the  extremities  of  the  bifurcated  ends  of  the  arm,  #,  is 
another  shaft,  A,  on  which  there  is  a  small  pulley  and  to  which 
is  attached  the  needle,  i,  that  gives  the  desired  indications ;  a 
a  fine  silk  fiber  is  attached  at  one  end  to  one  of  the  arms  of,  #, 
then  passes  around  the  pulley  and  the  staff,  A,  and  finally  has 


MEASUREMENT   OF   CURRENT. 


179 


its  other  extremity  secured  to  the  other  arm.  The  arms  are 
springy  and  serve  to  keep  the  silk  fiber  taut.  The  current  to 
be  measured  flows  through  the  wire,  a,  only,  entering  and  leav- 
ing as  indicated  by  the  arrows.  Evidently,  when  a  is  heated 
by  the  passage  of  current,  it  expands,  which,  as  a  and  b  were 
originally  under  the  same  tension,  makes  a's  tension  relatively 
less  than  that  of  ft,  and  equilibrium  can  be  restored  only  when 
the  pulley,  J,  rotates  sufficiently  again  to  equalize  the  strain. 
The  rotation  of  c?,  of  course,  carries  g  with  it,  and  #,  in  moving, 
causes  the  silk  fiber  to  rotate  the  shaft  which  carries  the  needle. 
If  the  temperature  of  the  air  surrounding  the  instrument 
changes,  a  and  b  are  affected  alike,  and  their  resulting  equal 
expansion  simply  results  in  a  movement  of  the  plate,  c,  back  or 
forth  in  its  path  without  any  tendency 
to  rotate  the  pulley. 

Among  the  advantages  of  the  above 
construction  is  the  fact  that  the  mem- 
ber which  compensates  for  the  expan- 
sion of  the  active  wire,  due  to  the 
temperature  changes  of  the  surrounding 
atmosphere,  is  not  only  of  the  same 
material  as  the  expansion  wire  itself, 
but  is  actually  a  piece  of  the  same 
wire,  and  hence,  has  exactly  the  same 
mass  and  physical  characteristics.  The 
compensation  must,  therefore,  be  per- 
fect. 

The  entire  moving  system  shown  in 
Fig.  139  is  mounted  on  a  single  base 
plate,  free  to  rotate  over  a  small  angle 
round  a  heavy  shaft  secured  to  it  immediately  below  and  in  line 
with  shaft,  A,  around  which  the  needle  swings.  This  enables 
one  to  alter  the  position  of  the  needle  relative  to  the  scale 
without  interfering  with  any  of  the  mechanism  in  any  way.  A 
complete  instrument  of  this  type  is  shown  in  Fig.  140. 

ELECTROSTATIC    AMMETERS. 

An  electrostatic  instrument  may  theoretically  be  used  for 
measuring  current  in  connection  with  a  shunt,  just  as  current 
is  measured  with  ammeters  of  the  permanent  magnet  type  as 


FIG.  139. 


180      ELECTRIC   AND  MAGNETIC  MEASUREMENTS. 

described  on  page  161.  Owing,  however,  to  the  fact  that  elec- 
trostatic instruments  require  a  considerable  potential  difference 
for  their  operation,  and  that  such  instruments  must  be  of  the 
fiber  suspended  instead  of  the  pivot  borne  type,  they  can  hardly 
be  said  to  come  under  the  head  of  commercial  measuring  appa- 
ratus, and  are  mentioned  here,  simply  to  keep  the  scheme  of 
treatment  intact.  If,  in  special  cases,  a  delicate  electrostatic 
voltmeter  be  available,  it,  in  connection  with  a  shunt,  evidently 
forms  a  means  of  measuring  the  strengths  of  either  direct  or 
alternating  currents,  but,  in  the  latter  case,  care  must  be  taken 


FIG.  140. 


that  the  shunt  across  which  the  drop  is  measured  has  no  self- 
induction,  for,  if  this  be  present,  the  drop  will  be  in  excess  of 
the  IR  drop,  and  the  indications  correspondingly  greater  than 
they  should  be. 

When  used  for  alternating  current  measurements  alone,  the 
difference  of  potential  necessary  to  operate  the  electrostatic 
meter  may  conveniently  be  made  of  much  higher  value  by  sub- 
stituting for  the  simple  shunt,  a  transformer,  whose  primary  is 
inserted  in  the  line  as  a  shunt,  and  which  is  so  designed  that  a 
rise  in  the  strength  of  the  current  flowing  through  the  primary 
winding  causes  a  corresponding  rise  in  the  E.M.F.  delivered 


MEASUREMENT  OF  CURRENT. 


181 


by  the  secondary.  The  objection  to  this  expedient  is  the  fact 
that  the  accuracy  is  dependent  on  the  frequency,  and  that  the 
transformation  ratio  of  the  transformer  is  exceedingly  high. 


AMMETERS    FOR    ALTERNATING   CURRENTS    ONLY. 

Induction  Ammeters. 

It  is  a  well-known  fact  that,  if  a  mass  of  conducting  material 
be  placed  within  the  influence  of  two  alternating  magnetic  fields 
which  vary  in  intensity  and  direction  at  the  same  rate,  but 
whose  maxima  and  minima  do  not  occur  simultaneously,  the 
reaction  between  the  currents  thus  set  up  in  the  mass,  and  the 
magnetic  fields  respectively,  will,  if  the  former  is  suitably  jour- 
naled,  tend  to  set  it  in  rotation.  This  principle  may  be  utilized 


FIG.  141. 


in   various    ways    in   the  construction    of   alternating  current 
instruments. 

Referring  to  Fig.  141,  if  A  be  a  disk  of  copper,  or  aluminum, 
one  portion  of  which  is  embraced  between  the  ends  of  a 
(7-shaped  structure  of  laminated  iron,  about  one  of  whose  legs 
wire  is  wound,  and  if  D  be  another  coil  of  wire  without  an  iron 
core,  and  the  two  windings  are  connected  to  a  source  of  current 
as  shown,  a  torque  tending  to  rotate  the  disk  A  is  set  rp  be- 
cause the  currents  in  the  two  coils  are  out  of  phase,  owing  to 
their  different  inductances.  If  the  tendency  of  A  to  rotate 
under  these  conditions  be  opposed  by  a  volute  spring  and  a 
pointer  be  attached  to  the  disk,  the  scale  over  which  the  pointer 
would  play  may  then  obviously  be  calibrated  directly  in  units 


182       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


of  current  strength  by  comparison  with  suitable  current 
standards. 

The  phase  difference  between  the  two  alternating  magnetic 
fields  may,  of  course,  be  brought  about  in  various  ways.  Fig. 
142,  for  instance,  shows  a  disk  of  conducting  material  arranged 
so  as  to  be  rotatable  between  the  jaws  of  a  (7-shaped  structure 
of  laminated  iron.  The  structure  has  a  hood  of  conducting  but 
non-magnetic  material  let  into  the  ends  of  the  (7,  extending  over  a 
portion  of  the  faces  so  that  the  currents  set  up  therein  distort 
the  magnetic  field  at  that  point,  and,  in  turn,  exert  a  force  tend- 
ing to  cause  the  disk  to  rotate  in  well-known  "shading  coil" 
fashion.  As  in  the  preceding  instrument,  the  extent  to  which 

the  disk,  or  the  pointer 
thereto  attached,  ro- 
tates over  affixed 
scale,  may  be  used  as 
a  measure  of  the  cur- 
rent strength. 

In  both  of  the  in- 
struments just  des- 
cribed, itis  convenient 
todamp  the  movement 
of  the  disk  and  render 
the  indications  of  the 
apparatus  dead  beat 
by  arranging  a  per- 
manent magnet  so 
that  the  disk  may 

rotate  between  its  polar  extremities,  and  Avhich,  therefore,  acts 
as  a  magnetic  brake.  Likewise,  both  must  be  calibrated  for 
the  frequency  on  which  they  are  to  be  used,  as  the  torque  is 
dependent  thereon,  and  both  are  subject  to  marked  errors 
when  exposed  to  varying  temperatures  because  of  the  high 
temperature  coefficient  of  the  material  of  which  the  rotating 
elements  are  necessarily  made. 

Induction  types  of  instruments  are  in  fairly  extended  use  in 
this  country,  but  it  can  hardly  be  said  that  their  results  are 
dazzlingly  accurate  or  satisfactory  as  compared  with  those  of  a 
good  iron  core  solenoid  device. 


FIG.  142. 


MEASUREMENT  OF  CURRENT. 


183 


SERIES    TRANSFORMERS. 

Owing  to  the  relatively  large  energy  consumption  of  alter- 
nating current  ammeters  of  the  electromagnetic  and  induction 
types,  and  to  certain  other  reasons  to  be  explained  further  on,  it 
is  not  usual  to  employ  shunts  to  furnish  the  drop  necessary  to 
actuate  them,  but  to Jnstall  instead  transformers  whose  primary 
windings  are  connected  in  series  with  the  supply  line,  the  sec- 
ondary terminals  being  attached  to  the  instrument.  This  is  con- 
venient when  heavy  currents  are  to  be  measured,  as  it  obviates 
the  necessity  of  winding  the  instrument  with  wire  heavy  enough 
to  carry  the  total  current  and  the  expense  that  is  frequently 


FIG.  143. 


involved  for  the  conductors  that  convey  the  current  to  and  from 
the  instrument.  It  is  also  of  value  where  the  measured  current 
is  supplied  under  high  potentials  dangerous  to  human  life,  as  the 
insulation  between  the  two  windings  of  the  transformer  may  be 
made  to  withstand  any  desired  voltage  so  that  that  of  the  cur- 
rent passed  through  the  meter  is  perfectly  innocuous. 

Series  transformers  must  be  designed  so  that  the  ratio  uf  the 
currents  in  their  two  windings  remains  practically  the  same  at 
any  load,  differing  in  that  respect  from  the  ordinary  lighting  trans- 
formers where  the  potential  ratio  is  the  one  that  it  is  desired  to 
keep  constant.  Typical  forms  are  shown  in  Figs.  143,  144, 


184       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

and  145,  perspective  and  cross-sectional  views  being  given. 
The  transformer  in  the  first  figure  is  of  the  cable  type  in 

which  the  primary 
winding  is  a  straight 
section  of  the  conduc- 
tor carrying  the  cur- 
rent to  be  measured, 
while  the  secondary 
winding  is  formed 
of  several  turns  of 
finer  wire  laid  parallel 

FIG  144  to  it.     In  the  second 

form    of  transformer, 

the  primary  winding  incloses  the  secondary,  while  in  the  third, 
the  structure  is  similar  to  that  of  the  ordinary  lighting  ^trans- 
former, but  instead  of  having  the  primary  windings  make  sev- 


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PiA  A  A  A  A  A  A  A  A 

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=^=j 

JOQQQOQQ&& 

w 

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© 

© 

* 

© 

© 

© 

FIG.  145. 


eral  turns  about  one  side  of  the  iron  core,  it  passes  straight 
through  it,  being  thus  in  effect  a  half  turn,  although  this  is,  of 
course,  completed  to  make  a  full  turn  by  the  return  circuit 
from  the  load  as  formed  by  the  other  bus-bar.  All  have  a 
transformation  ratio  that  varies  somewhat  with  the  varying 
frequencies,  and  hence,  all  must  be  calibrated  for  the  number 
of  alterations  on  which  they  are  to  be  used. 


MEASUREMENT  OF  CURRENT.  185 


SHUNTS    FOR  ALTERNATING  CURRENT  INSTRUMENTS. 

As  mentioned  above,  shunts  are  sometimes  used  in  connection 
with  alternating  current  ammeters,  this  being  done  when  there 
is  no  necessity  for  interposing  a  high  insulation  between  the 
instrument  winding  and  the  current  carrying  conductors,  and 
when  the  instrument  is  of  a  type  sufficiently  sensitive  to  be 
actuated  by  the  drop  across  a  shunt  of  commercial  dimensions. 
As  instruments  sufficiently  sensitive  to  use  on  these  drops  are 
usually  of  the  hot  wire  pattern  in  which  the  inductance  is  low, 
it  is  a  matter  of  small  difficulty  to  make  the  design  such  that 
the  ratio  of  the  inductance  to  the  resistance  of  the  shunt  and 
the  instrument  are  equal  so  that  the  frequency  of  the  current 
being  measured  introduces  no  error,  and  the  apparatus  may  be 
used  on  either*  direct  or  alternating  current  without  its  being 
necessary  to  employ  correction  factors,  or  draw  in  additional 
scales. 

Very  particular  care  must,  however,  be  taken  to  make  the 
resistance  of  the  joints  between  the  instrument  terminals  and 
the  shunt  a  minimum,  as  the  instrument  circuit  resistance  is 
already  low,  and  if  that  of  the  joints  is  comparable  thereto,  an 
error  is  introduced. 

CALIBRATION  OF  AMMETERS. 

SOURCE    OF   CURRENT. 

In  calibrating  an  ammeter,  the  first  matter  to  consider  is  the 
source  from  which  the  testing  current  may  be  drawn.  In  all 
cases,  it  is  desirable  to  have  this  source  of  low  potential,  as 
otherwise  it  is  necessary  to  employ  bulky  and  expensive  auxil- 
iary apparatus,  such  as  rheostats  or  other  resistances,  across 
which  the  portion  of  E.M.F.  not  required  to  force  the  current 
through  the  instrument  may  be  dropped.  For  the  calibration  of 
direct  current  instruments,  this  means  that  the  most  suitable 
current  source  is  either  a  low  voltage  dynamo,  such  as  is  used 
for  electroplating  work,  or  else  one  or  two  large  storage  battery 
cells.  The  electroplating  dynamo  is  convenient  when  a  source 
of  power  maintaining  a  steady  speed  is  available,  because  the 


186        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

E.M.F.  which  it  generates,  and  hence,  the  current  which  it  will 
force  through  the  instrument  under  test,  is  very  easily  regu- 
lated by  means  of  an  inexpensive  rheostat  placed  in  its  field 
circuit.  Unfortunately,  however,  plating  dynamos  are  not  com- 
monly at  hand,  or,  if  one  is,  the  speed  of  the  pulley  that  drives 
it  may  be  so  irregular  that  the  current  cannot  be  held  steady  for 
a  sufficient  length  of  time  to  make  the  necessary  observations. 
A  storage  battery,  therefore,  forms  the  source  most  commonly 
used,  and  has  the  great  advantage,  that  for  the  short  periods  of 
time  during  which  current  is  being  drawn  in  making  compari- 
sons between  the  tested  instrument  and  the  standard,  it  will 
deliver  a  current  considerably  in  excess  of  its  normal  discharge 
rate  without  injury. 

When  testing  alternating  current  ammeters,  the  current 
source  may  be  any  alternating  current  dynamo,  as  the  potential  at 
which  current  is  delivered  may  readily  be  stepped  down  by 
means  of  a  transformer,  to  any  suitable  figure,  the  current 
strength  at  the  same  time  being  raised  to  a  correspondingly 
higher  value.  Adjustable  impedances  are  then  employed  to 
vary  the  amperage  over  the  range  needed  in  the  checking  of  the 
particular  instrument  under  test. 


CURRENT   REGULATING   DEVICES. 

In  order  to  be  able  to  adjust  the  strength  of  the  current 
passed  through  the  instrument  under  test,  and  to  hold  it  con- 
stant at  any  desired  point  for  a  reasonable  length  of  time,  it  is 
usual  to  employ  resistances  whose  construction  varies  somewhat, 
according  to  whether  the  currents  are  large  or  small.  In  the 
latter  event,  common  wire  resistances  or  rheostats  of  any  con- 
ventional form  are  employed,  it  being  advisable  to  select  those 
in  which  the  resistance  wire  is  of  a  metal  having  a  very  small 
temperature  coefficient,  so  that,  when  it  is  heated  by  the  passage 
of  current,  its  resistance  may  not  change  sufficiently  to  necessi- 
tate a  constant  readjustment.  Such  rheostats  are  usually  pro- 
vided with  contact  plates,  so  it  is  possible  to  get  only  as  many 
different  current  strengths  as  there  are  contacts.  Sometimes, 
however,  the  resistance  wires,  or  bars,  are  arranged  so  as  to  be 
accessible  throughout  their  length  and  a  sliding  contact  pro- 
vided with  a  clamp  is  fitted  to  them ;  so  that  good  contact  may 


MEASUREMENT  OF  CURRENT. 


187 


be  made  at  any  desired  point,  and  hence,  gives  an  infinite  num- 
ber of  steps. 

Another  form  of  rheostat,  whose  resistance  may  be  varied  by 
imperceptible  gradations,  is  built  up  of  carbon,  which  may  be  in 
the  form  of  carbon  grains  contained  within  an  elastic  envelope, 
capable  of  being  compressed,  to  a  greater  or  less  extent,  between 
a  fixed  terminal  plate  and  a  movable  one.  A  rheostat  of  this 
kind  is  shown  in  Fig.  146.  Where  the  currents  are  heavier, 
carbon  rheostats  are  made  by  placing  the  broad  faces  of  a 
number  of  carbon  blocks  in  contact  with  one  another,  and 
enclosing  them  in  a  framework  that  is  equipped  with  a  screw, 


FIG.  146. 


by  means  of  which  they  may  be  pressed  together  more  or  less 
firmly.  The  greater  the  pressure,  the  less  the  resistance.  A 
rheostat  of  this  kind  is  shown  in  Fig.  147. 

Plain  (not  coppered)  arc  light  carbons  may  be  used  to  make 
a  temporary  rheostat  along  the  same  lines  by  placing  them  on 
end  in  an  asbestos-lined  perforated  bottomed  box,  as  shown  in 
Fig.  148.  The  two  ends  of  the  box  are  provided  with  large 
terminal  sheets  of  brass,  one  of  which  can  be  pushed  inward  by 
turning  the  crank  handle  shown.  The  large  radiating  surface  left 
by  the  interstices  between  the  carbon  rods  enables  this  rheostat 
to  carry  comparatively  heavy  currents,  but,  in  common  with 
the  two  preceding  forms,  it  labors  under  the  disadvantage  that 
the  possible  range  of  variation  in  resistance  is  rather  small. 


188       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


For  laboratory  work  in  handling  heavy  currents,  a  very  con- 
venient form  of  resistance  is  made  up  of  German  silver  tubing 


FIG.  147. 

^ 

through  which  a  stream  of  water  from  the  city  mains  is  con- 
stantly flowing.  The  direction  of  the  water  flow  should  be 
from  the  lower  to  the  upper  part  of  such  a  tube  in  order  to  do 
away  with  the  chance  of  having  the  tube  fused  if  the  water 

supply  should  momenta- 
rily fail.  By  using  this 
artificial  cooling  method, 
there  can  be  carried  from 
fifteen  to  twenty  times  the 
amount  of  current  that 
would  be  possible  without 
it.  The  plan  does  not 
introduce  difficulties  be- 
cause of  the  grounding 
of  the  current  source 
through  the  stream  of 

water  which  flows  from  the  city  mains  if  a  few  feet  of  rubber 
tubing  are  interposed  between  the  mains  and  the  German  silver, 
as  the  resistance  of  a  column  of  water  of  that  length  renders 
impossible  the  passage  of  any  appreciable  amount  of  current 
with  the  E.M.F.'s  usually  available  in  ammeter  testing. 

The  current  supplied  for  testing  alternating  current  ammeters 
may,  of  course,  be  regulated  by  the  same  devices  used  for  direct 
current.  Where  many  alternating  instruments  are  to  be  cali- 
brated, however,  it  is  cheaper  to  effect  the  regulation  either  by 


FIG.  148. 


MEASUREMENT  OF  CURRENT.  189 

means  of  leads  tapped  out  from  the  primary  windings  of  a 
transformer  from  which  the  current  supply  is  drawn,  and  in 
this  way  varying  the  ampere  turns  of  the  primary,  or,  better 
still,  by  introducing  in  the  primary  circuit  an  adjustable  in- 
ductance or  "  kicking  coil "  such  as  is  used  for  alternating 
current  theater  dimmers. 

METHODS    OF    CALIBRATION    OF   AMMETERS. 

Voltameter  Method. 

In  spite  of  the  fact  that  the  value  of  an  ampere  is  denned  by 
the  International  Congress  in  terms  of  the  performance  of  a 
silver  voltameter,  neither  this  nor  the  more  easily  used  copper 
voltameter  is  commonly  employed  in  the  calibration  of  ammeters 
owing  to  the  cumbersome  nature  of  the  voltameter  itself  and  to 
the  numerous  precautions  that  must  be  taken  to  avoid  the 
errors  which  may  creep  in,  due  to  inaccurate  observation  of 
elapsed  time,  error  in  weighing  the  plates,  and  the  necessity 
of  maintaining  the  current  strength  absolutely  uniform  for 
many  minutes.  The  method  is,  further,  a  very  slow  one ; 
so  that,  while  it  may  be  used  in  laboratories  for  the  calibration 
of  secondary  standards,  it  is  out  of  the  question  to  employ  it 
commercially  in  testing  a  number  of  instruments.  The  stand- 
ards ordinarily  used  are,  hence,  either  of  the  secondary  class, 
which  must  initially  be  graduated  by  comparison  with  a  primary 
instrument,  but  which  are  so  constructed  that  they  contain  no 
parts  liable  to  change  with  lapse  of  time,  or  one  like  the  poten- 
tiometer, giving  ampere  values  derived  from  standards  of 
resistance  and  E.M.F. 

In  both  cases  the  apparatus  shows  the  instantaneous  values 
of  the  test  current,  and  not  the  product  of  its  mean  value  by 
elapsed  time. 

Calibrating  with  a  Balance  or  a  Dynamometer. 

The  secondary  standard  is  usually  either  an  ampere  balance 
of  the  Kelvin  type  described  on  page  18  or  a  Siemens  Dyna- 
mometer as  described  on  page  165.  The  former  gives  closer 
readings,  because  of  its  great  scale  length ;  and  it  is  less  likely 
to  change,  since  only  its  geometrical  dimensions,  the  value  of 
gravitational  attraction,  and  the  integrity  of  its  windings  can 


190      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

affect  its  indication,  when  properly  installed.  The  dynamometer 
employs  spring  torsion  instead  of  gravity  for  an  opposing  force, 
and  spring  elasticity  may  change.  These  springs  are,  however, 
made  so  long  and  worked  so  far  within  their  limits  of  elasticity 
that  an  error  due  to  a  sudden  change  in  that  quality  is  extremely 
improbable.  While  their  scale  length  is  less  than  that  of  a 
balance,  they  are  more  portable,  less  care  need  be  taken  to  obtain 
a  vibrationless  foundation,  and  readings  may  be  taken  with 
much  greater  rapidity.  The  results  are,  with  ordinary  care, 
sufficiently  accurate  for  all  commercial  purposes. 

Calibration  with  a  Potentiometer. 

The  chapter  on  the  potentiometer  has  explained  how  this 
instrument  may  be  used  as  a  standard  in  the  measurement  of 
direct  currents.  Giving,  as  it  does,  results  in  terms  of  the 
E.M.F.  of  a  standard  cell,  and  dependent  only  on  this  and  the 
accuracy  of  the  standard  resistance  across  which  the  drops  are 
measured,  the  results  obtainable  with  a  potentiometer  are 
thoroughly  trustworthy,  if  reasonable  care  be  employed.  By 
having  a  set  of  two  or  three  standard  resistances,  and  of  two  or 
three  standard  cells,  all  of  which  may  be  checked  against  one 
another,  it  is  almost  inconceivable  that  errors  greater  than  those 
introduced  by  the  inherent  limitations  of  the  apparatus  could 
enter,  particularly  as  the  method  is  a  zero  one,  and  does  not 
depend  upon  the  constancy  of  the  indications  of  any  current  actu- 
ated device.  The  potentiometer  is  always  to  be  preferred  for 
checking  direct  current  ammeters  if  one  is  available. 

Calibration  of  Alternating   Current  Ammeters. 

An  alternating  current  ammeter  measures  effective  current 
strengths,  that  is  to  say,  when  it  indicates  a  given  number  of 
amperes  flowing  from  an  alternating  current  source,  it  means 
that  that  current  in  flowing  through  a  given  circuit  would  ex- 
pend therein  the  same  amount  of  energy  that  a  continuous  current 
of  the  same  amperage  would  expend  in  flowing  through  the 
same  circuit  and  doing  the  same  amount  of  work. 

A  hot  wire  type  ammeter,  therefore,  in  which  the  energy  is 
expended  in  heating  a  resistance  wire,  after  being  calibrated 


MEASUREMENT  OF  CURRENT.         191 

with  continuous  current,  may  be  used  to  measure  alternating  cur- 
rent amperes,  and  as  a  secondary  standard  for  the  calibration  of 
other  alternating  current  instruments.  In  a  similar  manner  the 
electro-dynamometer  and  the  Kelvin  balance,  in  which  the  current 
energy  is  expended  in  keeping  a  spring  stressed,  or  sustaining  a 
weight  against  the  attractive  force  of  gravity  respectively,  after 
being  first  calibrated  with  continuous  currents,  may  be  used  to 
standardize  other  instruments  for  the  measurement  of  alternat- 
ing current  amperes. 

When  using  the  hot  wire  type  of  meter  for  a  transfer  standard 
of  this  nature,  it  is  desirable  to  check  its  calibration  with  direct 
current,  both  immediately  before  and  immediately  after  the 
measurement,  as  most  designs  have  the  unfortunate  character- 
istic of  lack  of  constancy  of  accuracy,  so  that  confidence  in  their 
indications  can  only  be  obtained  as  outlined.  With  the  dyna- 
mometer patterns  of  meters  the  calibration  is  more  stable,  but 
the  conductors  to  and  from  them  must  be  twisted  together  to 
form  a  cable,  in  order  to  avoid  inductive  influences,  and  their 
windings  must  be  finally  laminated  in  order  that  the  distribution 
of  current  through  them  may  be  the  same,  whether  that  current 
be  direct  or  alternating. 

Precautions. 

If  the  ammeter  under  test  be  of  the  electromagnetic  type, 
errors  due  to  changes  in  its  temperature  do  not  enter  to  an 
appreciable  extent,  since  the  number  of  turns  of  the  actuating 
solenoid  remains  constant,  and  the  whole  current  flowing  through 
this  influences  the  iron  core  to  the  same  extent,  whether  the  re- 
sistance of  the  windings  be  high  because  of  a  high  temperature, 
or  low  because  of  a  low  one.  Thus,  the  only  effect  of  varying 
temperature  is  to  cause  a  varying  drop  across  the  instrument 
terminals. 

On  the  other  hand,  electromagnetic  instruments  work  by 
magnetic  attraction  on  iron,  and  the  property  of  iron,  known  as 
hysteresis,  by  virtue  of  which  the  flow  of  the  lines  of  force 
through  it  is  dependent,  not  on  the  magnetizing  force  alone, 
but  also  on  the  magnetic  stress  to  which  it  was  previously  sub- 
ject, introduces  an  error.  If  the  attractive  magnetic  force  is  at- 
tained by  increasing  the  strength  of  an  already  existing  current 


192     ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

to  a  given  new  value,  the  pull  on  the  iron  core  of  the  instru- 
ment is  less  than  if  the  same  value  were  reached  by  decreasing 
a  larger  current  to  that  amount,  and  the  instrument  needle, 
therefore,  has  different  positions  to  indicate  the  same  current 
strength.  The  amount  of  difference  depends  on  the  design  of 
the  apparatus  and  the  quality  of  the  iron  employed  and  is  very 
small  in  good  instruments.  In  others,  however,  the  error  is 
large,  and  it  is,  therefore,  necessary,  in  checking  the  calibration 
of  an  electromagnetic  ammeter,  to  make  two  sets  of  observa- 
tions, one  with  an  increasing,  and  the  other  with  a  decreasing, 
series  of  values  to  fully  determine  its  characteristics. 

If  the  ammeter  to  be  tested  be  of  the  d'Arsonval  type,  in 
which  there  is  a  stationary  permanent  magnet,  and  a  moving 
coil  of  wire  which  carries  a  known  fraction  of  the  current  to  be 
measured,  this  particular  source  of  error  is  not  present,  sin^e  the 
wire  is  non-magnetic  and  non-hysteretic.  On  the  other  hand, 
temperature  influences  enter,  since  the  materials  entering  into 
the  composition  of  the  two  branches  of  the  circuit,  formed  by 
the  instrument  and  its  shunt  respectively,  are  different,  and  their 
temperature  coefficients  differ  likewise  ;  so,  when  the  tempera- 
ture is  other  than  that  at  which  the  calibration  was  initially 
effected,  the  ratio  of  the  currents  flowing  through  the  two, 
changes.  This  matter  has  been  treated  more  fully  in  the  sec- 
tion on  shunts  (see  page  162)  to  which  reference  should  be  made. 
For  work  of  high  accuracy  with  d'Arsonval  instruments  it  is 
preferable  to  have  a  shunt  with  a  zero  temperature  coefficient 
and  an  instrument  whose  variation  of  resistance  with  variations 
of  temperature  is  known,  as  appropriate  corrections  for  the  in- 
strument temperature  can  then  readily  be  applied. 


CHAPTER  VII. 

MEASUREMENT   OF   POTENTIALS. 

DIRECT  CURRENT  E.M.F.'S. 

MEASUREMENT    WITH    THE   POTENTIOMETER. 

THE  paragraph  on  the  potentiometer  (page  73)  has  explained 
how  this  apparatus  is  used  in  measuring  an  E.M.F.  in  terms  of 
the  difference  of  potential  existing  between  the  terminals  of 
a  standard  cell.  While  it  is  not  necessary  to  enlarge  further 
on  the  apparatus  here,  it  may  be  reiterated  that  this  method  is 
capable  of  the  highest  commercial  accuracy  and  involves  the  use 
of  apparatus  that  is  comparatively  inexpensive  and  exceedingly 
reliable. 

MEASUREMENT    WITH    PERMANENT    MAGNET    VOLTMETERS. 

All  indicating  voltmeters,  with  the  exception  of  those  of 
the  electrostatic  type  to  be  treated  further  on,  are  nothing  but 
ammeters  of  very  high  resistance  and  capable  of  measuring  only 
minute  currents.  That  such  an  ammeter  can  be  calibrated  to 
indicate  voltage  instead  of  amperage  is  evident  from  a  con- 

W 

sideration  of  Ohm's  law,  I  —  — .     If  in  this  formula  R  is  a 

±i 

constant  quantity  and  of  a  value  so  high  that  the /drawn  from  the 
circuit  does  not  disturb  the  potential  difference,  E,  at  the  points 
of  attachment  of  the  meter's  terminals,  E  becomes  directly  pro- 
portional to  /,  and  a  given  ammeter  may,  therefore,  be  calibrated 
in  volts  instead  of  amperes.  This  general  remark  should  not 
be  interpreted  to  mean  that  an  indicating  voltmeter  is  built 
exactly  like  an  indicating  ammeter ;  on  the  contrary,  the  require- 
ments are  diametrically  opposed.  In  the  ammeter  it  is  desirable 
to  have  the  resistance  of  the  instrument  a  minimum  in  order 
that  the  drop  across  its  terminals  may  be  as  small  as  p  *ssible, 
and  the  largest  possible  remaining  E.M.F.  left  available  to  force 
the  current  through  the  external  circuit,  whereas,  in  a  voltmeter, 
the  resistance  is  made  as  high  as  can  be  done  in  order  that  the 
current  it  draws  may  be  a  minimum  and  not  appreciably  reduce 

193 


194        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

the  potential  between  the  points  of  attachment.  Further,  with 
ammeters  of  the  shunt  pattern,  the  potential  available  for  forc- 
ing the  current  through  the  instrument  windings  is  only  that 
due  to  the  drop  in  potential  across  the  terminals  of  the  instru- 
ment shunt  because  of  the  resistance  of  that  shunt,  and  that 
resistance  must  be  kept  very  low  in  order  that  this  portion  of 
the  instrument  may  not  become  too  bulky  and  costly,  whereas, 
in  a  voltmeter,  the  majority  of  commercial  potentials  that  have 
to  be  measured  are  comparatively  high,  usually  well  in  excess 
of  1  volt,  so  that  that  amount  of  E.M.F.  may  be  dropped  across 
the  windings  of  the  active  coil  proper.  One  other  feature  is 
that  in  shunt  ammeters,  owing  to  the  errors  introduced  by 
varying  temperature  of  the  instrument  windings,  conservative 
current  densities  must  be  employed  in  order  to  prevent  the 
current  flowing  through  them  from  causing  a  sufficient  tempera- 
ture rise  to  introduce  in  itself  appreciable  errors.  Such  is  not 
the  case  with  voltmeters.  Here  1  to  3  volts  is  the  ordi- 
nary drop  across  the  active  coil  terminals,  this  figure  being 
imposed  by  the  fact  that  instruments  of  this  low  range  are 
sometimes  required,  and  by  the  additional  fact  that  to  obtain  a 
greater  one  windings  would  have  to  be  used  of  a  diameter  so 
small  as  to  render  their  employment  almost  impossible  for 
mechanical  reasons.  A  large  auxiliary  resistance  must  be  con- 
nected in  series  with  the  active  coil  itself,  therefore,  in  order 
that  it  may  drop  all  of  the  potential  except  the  1  to  3 
volts  required  by  the  coil  windings,  and  the  temperature  coeffi- 
cient of  that  resistance  may  be  selected  so  as  to  make  the 
apparatus,  as  a  whole,  practically  independent  of  temperature 
influences.  Suppose,  for  instance,  that  the  instrument  in  ques- 
tion is  of  150  volts  capacity  and  that  1£  volts  potential  at  the 
active  coil  terminals  would  cause  full  scale  deflection ;  the 
temperature  coefficient  of  the  coil  circuit  would  probably  be 
about  that  of  copper,  i.e.,  the  resistance  would  increase  about 
1  per  cent,  for  a  temperature  rise  of  5°.  If  the  resistance 
that  was  placed  in  series  with  this  active  coil,  in  order  to  make 
it  necessary  to  apply  150  volts  potential  difference  to  the 
terminals  to  give  full  scale,  is  of  a  metal  having  a  zero  tem- 
perature coefficient,  a  change  of  5°  in  the  temperature  of 
the  instrument  would  mean  a  change  in  the  resistance  of  the 
instrument  as  a  whole,  not  of  1  per  cent,  but  of  .01  per  cent. 


MEASUREMENT  OF  POTENTIALS.  195 

in  other  words,  for  ordinary  temperature  changes  the  error  is 
entirely  negligible. 

With  the  foregoing  differences  between  a  voltmeter  and  an 
ammeter  understood,  a  reference  to  the  chapter  on  ammeters  of 
the  permanent  magnet  type  will  explain  sufficiently  the  similar 
direct  current  voltmeters. 

VOLTMETERS  FOR  BOTH  DIRECT  AND  ALTERNATING  CURRENT. 

VOLT  BALANCES. 

The  Kelvin  balances  that  have  been  described  in  the  chapter 
on  laboratory  and  commercial  standards  and  mentioned  in  the 
chapter  on  ammeters,  can  be  used  for  the  measurement  of  po- 
tentials also.  For  this  work  the  centi-ampere  balance  is  chosen, 
as  this  demands  the  least  amperage  for  its  operation  and  is  of 
the  highest  resistance.  The  manufacturers  supply  resistances 
made  of  low  temperature  coefficient  metal  to  be  used  in  connec- 
tion with  the  centi-ampere  balance  to  enable  its  employment  in 
the  measurement  of  commercial  voltages.  As  in  these  devices 
the  percentage  of  the  total  instrument  circuit  resistance  offered 
by  the  copper  balance  coils  is  high,  it  is  necessary  to  use  in 
connection  with  it  thermometers  that  show  the  coil  temper- 
atures and  to  make  proper  allowance  for  any  deviation  from  the 
normal  at  which  calibration  was  effected  if  accurate  results  are 
to  be  had. 

EEFLECTING    ELECTROMETERS. 

The  reflecting  electrometer  has  been  mentioned  on  page  30. 
It  forms  an  ideal  device  for  the  measurement  of  potentials  in 
that,  as  its  resistance  is  infinitely  high,  no  current  is  drawn 
from  the  source  under  test,  and  the  potential  shown  is,  therefore, 
that  of  the  source  when  on  open  circuit. 

It  is  not,  however,  common  to  use  such  meters  for  the  meas- 
urement of  low  potentials,  as  they  can  hardly  be  said  to  be  of  a 
commercial  pattern ;  the  moving  element  is  fiber  suspended  and 
hence  not  portable,  and  the  indications  must  be  read  off  v\  ith  a 
telescope  and  scale,  or  a  lamp  and  scale,  which  does  not  make 
the  operation  any  more  easy.  When  a  reflecting  electrometer  is 
to  be  used,  it  should  first  be  tested  on  direct  current  by  attach- 
ing to  its  terminals  a  battery  of  low  E.M.F.,  observing  the 
deflection,  reversing  battery  connections,  and  observing  the  fresh 


196       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

deflection  and  then  comparing  notes.  In  the  case  o*f  the  great 
majority  of  electrometers  it  will  be  found  that  the  two  indica- 
tions do  not  agree.  This  is  because  the  suspension  supporting 
the  moving  vanes  is  necessarily  an  electrical  conductor  and 
almost  invariably  of  different  metal  from  that  forming  the 
vanes,  the  former  being  ordinarily  of  phosphor-bronze  strip  and 
the  latter  of  sheet  aluminum.  When  dissimilar  metals  are  in 
contact  a  difference  of  potential  exists  between  them,  and,  al- 


FiG.  149. 


though  this  is  small,  it  is  comparable  with  that  of  potentials 
within  the  range  of  measurement  of  the  electrometer.  The 
instrument  will,  therefore,  read  higher  with  the  outside  polarity 
presented  in  one  way  than  when  connections  to  it  are  reversed, 
so  that  if  it  was  originally  calibrated  on  direct  current  it  should 
always  have  a  given  binding-post  attached  to  the  direct  current 
terminal  of  the  same  polarity  as  when  originally  calibrated. 
When  used  for  measuring  an  alternating  E.M.F.  the  electrom- 
eter will  read  high  or  low  by  an  amount  equal  to  the  contact 
E.M.F.  between  the  suspension  and  the  vane.  It  will  read 
high  if  the  calibration  with  direct  current  was  effected  with  the 


MEASUREMENT   OF   POTENTIALS.  197 

outside  E.M.F.  opposing  the  contact  E.M.F.,  and  low  if  the 
two  assisted  each  other.  A  proper  allowance  must,  of  course, 
be  made  for  this  factor. 

ELECTROSTATIC    VOLTMETERS. 

While  the  sensitive  fiber  suspended  reflecting  electrometers 
are  little  used  except  for  laboratory  purposes,  the  same  princi- 
ple is  employed  with  considerable  success  in  commercial  work 
where  the  potentials  involved  are  sufficiently  high  to  give  large 
deflecting  forces  of  a  magnitude  comparable  with  those  existing 
in  electromagnetic  or  permanent  magnet  instruments.  Other 
things  being  equal,  the  rotational  effort  exerted  on  the  moving 
element  varies  as  the  square  of  the  potential,  so  that  as  the 
potentials  increase,  the  point  at  which  sufficient  torque  is 
obtainable  is  rapidly  reached.  Where  the  potential  regularly 
used  is  too  low  to  give  the  desired  directional  effort  with  a 
single  pair  of  vanes  of  practicable  size,  the  number  of  pairs 
may  be  multiplied,  as  in  the  case  of  the  Kelvin  multicellular 
voltmeters  mentioned  on  page  32. 

Fig.  149  shows  a  similar  instrument  made  by  Hartmann  & 
Braun.  The  principal  difference  between  this  and  the  Kelvin 
instrument  is  in  the  shape 
of  the  movable  vanes  and 
in  the  fact  that  the  indi- 
cations are  damped  by  an 
aluminum  disk  swinging 
between  the  poles  of  a  per- 
manent magnet  instead  of 
a  disk  immersed  in  oil. 

Another  type  of  electro- 
static voltmeter  is  shown 
in  Fig.  150,  wherein  the 
vane  system  is  not  sym- 
metrical to  the  axis  about 
which  it  rotates,  and  the 
damping  is  accomplished 

by  means  of  an  air  vane  fitting  closely  in  a  nearly  tight  box. 
The  sensibility  of  this  pattern  of  meter  cannot  be  made  very 
great,  the  minimum  full  scale  voltage  for  which  they  can  be  con- 
structed being  1,000. 


198       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

As  electrostatic  voltmeters  are  as  a  rule  used  for  high  poten- 
tial work,  it  becomes  necessary  to  take  special  precautions  to 
prevent  a  spark  from  passing  from  the  fixed  to  the  movable 
elements.  The  distance  between  the  two  is  made  a  minimum 
in  order  that  the  actuating  force  may  be  as  large  as  possible, 
and  fuses  of  vpry  fine  wire  are  ordinarily  placed  in  the  instru- 
ment circuit  so  that  if  a  spark  should  pass,  the  current  flowing 
through  conducting  paths  thus  opened  will  blow  the  fuse  and 
disconnect  the  apparatus.  This  expedient  is,  however,  not 


FIG.  151. 

always  efficacious,  as  the  amount  of  current  is  but  small, 
and  the  apparatus  may  be  ruined  before  it  attains  a  strength 
sufficient  to  melt  the  safety  fuse.  Additional  protection  is 
afforded  by  enveloping  the  stationary  plates  in  a  coating  of 
mica  or  hard  rubber.  A  superior  plan  is  to  make  connection 
between  the  instrument  and  the  line,  not  directly,  but  through 
the  intervention  of  condensers  whose  insulation  resistance  may 
be  made  as  high  as  is  desired.  With  this  arrangement  it  is 
practically  impossible  to  burn  out  the  voltmeter,  if  properly 
designed. 

Electrostatic  voltmeters  per  se  are  not  in  common  use  in  this 


MEASUREMENT  OF  POTENTIALS.  199 

country,  but  instruments  based  on  the  electrostatic  principle  and 
used  to  indicate  the  occurrence  of  a  ground  on  high  potential 
lines  are  very  popular.  Such  devices  are  called  "  ground  de- 
tectors," and  one  is  shown  in  Fig.  151.  In  use  the  movable 
vane  is  electrically  connected  to  a  ground-wire,  and  the  dia- 
metrically opposite  fixed  quadrants  to  either  side  of  the  line. 
As  long  as  the  circuit  is  not  grounded,  the  potential  difference 
between  each  pair  of  quadrants  and  the  movable  element  is  the 
same,  and  the  index  points  to  zero.  Should,  however,  one  of 


FIG.  152. 


the  lines  become  wholly  or  partly  grounded,  the  potential  differ- 
ence between  the  quadrants  attached  to  that  wire  and  the  mov- 
able element  is  less  than  that  between  the  other  wire  with  its 
attached  pair  of  quadrants  and  the  same  movable  element,  so 
that  the  needle  is  deflected,  the  direction  of  the  deflection 
showing  the  side  of  the  line  that  is  faulty. 

Where  multiphase  circuits  are  used,  three  single-phase  elec- 
trostatic ground  detectors  like  the  above  are  often  employed,  and 
these  may  conveniently  be  built  into  a  common  case  as  is  shown 
in  Fig.  152. 

A  more  recent  instrument  makes  use  of  three  stationary 
plates  (in  a  three-phase  system)  placed  120°  apart,  each  con- 
nected to  one  of  the  line  wires.  At  the  center  of  the  spherical 


200       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


triangle  formed  by  these  plates  there  is  pivoted  so  as  to  be  mov- 
able toward  any  of  them,  a  fourth  vane  electrically  connected  to 
ground. 

It  is  evident  from  Fig.  153  that  if  any  one  of  the  three  line  wires 
becomes  grounded,  the  movable  vane  will  move  away  from  the 


FIG.  153. 

central    position    where    it    is    normally    held    by  the    springs 
shown,  because  the  original  equality  of  difference  of  potential 

between  each  fixed  vane  and 
the  moving  one  is  disturbed, 
and  that  the  deflection  of  the 
pivoted  vane,  therefore,  shows 
not  only  that  a  ground  has 
come  into  existence,  but  on 
which  of  the  conductors  it  is 
located.  A  perspective  view 
of  a  three-phase  ground  de- 
tector of  this  kind  is  given  in 
Fig.  154. 

An  electrostatic  ground  de- 
tector in  which  the  repulsion 
between  sharp  points  similarly  charged  is  used  instead  of  the 
attraction  between  flat  plates  oppositely  charged,  is  shown  in 
Fig.  155. 

In  all  electrostatic  voltmeters,  it  is  advisable  to  have  the  pro- 
tective   casing    of    metal    in    metallic  connection  with  a  well- 


FlG.  154. 


MEASUREMENT  OF  POTENTIALS.  201 

grounded  plate,  as  the  latter  then  serves  not  only  as  a  shield 
against  disturbances  due  to  foreign  electric  charges,  but  will 
prevent  injury  to  the  attendant  if  he  should  accidentally  come 
into  contact  with  the  meter. 


DYNAMOMETER    VOLTMETERS. 

As  in  the  case  of  other  types  of  ammeters  described  in  the 
preceding  chapter,  an  electrodynamometer  may  be  used 
to  measure  volt- 
ages by  forming  its 
coils  of  many  turns 
of  small  diameter 
wire  instead  of  a 
few  turns  of  wire  of 
large  cross-section. 
The  Siemens  dyna- 
mometer, as  illus- 
trated on  page  165, 
is  however  seldom 
used  in  its  original 
form  for  potential 
measurements,  as 
the  currents  in- 
volved are  so  small 
that  the  use  of 

mercury  cups  is  un-  FlG<  155 

necessary.        They 

are  usually  replaced  by  two  torsion  springs,  the  current  being  led 
into  and  out  of  the  moving  coil  through  these.  In  some  patterns 
there  is  but  one  spring,  a  very  flexible  conducting  strip  being 
employed  to  carry  the  current  away. 

A  typical  form  of  the  modified  electrodynamometer  class  of 
voltmeter  is  the  Weston  instrument,  whose  moving  element  is 
shown  in  Fig.  156.  As  will  be  noted,  this  consists  of  a  circular 
coil  of  many  turns  of  wire,  equipped  above  and  below  with 
pivots  which  rest  in  appropriate  jewel  bearings,  and  having  its 
coil  ends  in  electrical  contact  with  two  volute  springs  secured 
to  the  pivots.  As  the  outer  extremities  of  these  springs  are 
attached  to  stationary  terminals,  they  serve  as  an  opposing  force 


202       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

to  the  coil  motion.  This  circular  coil  is  placed  within  a  larger 
stationary  one  whose  windings  are  connected  in  series  with  it 
so  that  the  current  in  both  reverses  simultaneously,  and  the  re- 
sultant effort  is  to  urge  the  coil  to  rotate  in  a  given  direction. 

Such  instruments  cannot  have  their  indications  damped  by 
winding  the  movable  coil  on  a  metallic  framework  forming  a 
closed  electrical  circuit,  as  in  the  case  of  permanent  magnet 
instruments,  because,  if  this  were  done,  the  framework  would 
act  as  a  short-circuited  secondary  of  a  transformer  when  alter- 


nating  current  s  passed  through  the 
winding,  and  the  reaction  between 
the  current  induced  therein,  and 
that  of  the  fixed  winding,  would 
of  itself  cause  deflections  whose 
amounts  vary  not  alone  with  the 
impressed  E.M.F.  but  with  the 
frequency,  and,  to  a  lesser  extent, 
with  the  wave  form.  In  the  older 
Weston  instrument,  the  damping 
Fic  156  is  accomplished  by  a  friction  brush 

which  acts  adjustably  on  the  small 

disk  secured  to  the  lower  pivot,  as  shown  in  Fig.  156.  In  the 
later  Weston  model,  and  in  other  similar  instruments,  'the 
damping  is  accomplished  by  means  of  an  air  vane  moving  in  a 
nearly  closed  box. 

While  such  dynamometer  voltmeters  may  be  used  for  the 
measurement  of  E.M.F.'s  of  either  direct  or  alternating  current 
circuits,  they  are  open  to  certain  objections.  In  the  first  place, 
the  magnetic  field  furnished  by  the  stationary  winding  for  the 
movable  one  to  work  in  is  necessarily  of  feeble  intensity,  as 
compared  with  the  magnetic  field  in  direct  current  instruments, 
this  being  because  the  whole  of  the  magnetic  circuit  is  through 
air,  and  because  the  number  of  energizing  turns  must  be  kept 
down  for  reasons  to  be  explained  later.  A  weak  instrument 
field  means  that  the  apparatus  is  sensitive  to  the  influence  of 


MEASUREMENT  OF  POTENTIALS.  203 

neighboring  foreign  fields.  This  feature  is  of  no  importance, 
when  alternating  potential  is  being  measured,  as  then  the  direc- 
tion of  the  current  through  the  movable  element  is  being  con- 
tinuously reversed ;  an  external  field  that  would  cause  the 
indications  to  be  high  when  the  current  is  flowing  in  one  direc- 
tion exerts  an  equal  influence  to  make  the  indication  low  with 
the  current  flowing  in  the  reverse  direction,  and  the  average 
result  actually  indicated  is  correct.  With  direct  current,  how- 
ever, this  does  not  hold  good,  and  it  is  necessary,  therefore,  to 
make  two  readings  with  a  given  source  of  d.c.  E.M.F.,  one  so 
that  the  current  flows  through  the  apparatus  one  way,  and  the 
other  with  it  flowing  the  other  way,  and  to  take  the  mean  of  the 
two  to  arrive  at  the  correct  result.  To  be  sure,  a  dynamometer 
instrument  of  this  kind  may  be  orientated  until  its  indications 
are  the  same,  irrespective  of  the  polarity  of  the  attached  con- 
ductors, but  to  find  the  exact  position  is  a  tedious  matter,  and 
seldom  worth  while. 

Another  objectionable  feature  of  the  dynamometer  type  of 
voltmeters,  and  which,  in  fact,  applies  to  all  alternating  current 
voltmeters  except  those  of  the  electrostatic  type,  is  their  low 
resistance.  It  is  necessary  that  this  should  be  low,  because 
the  number  of  turns  must  be  kept  down  in  order  that  the  resist- 
ance offered  to  the  flow  of  a  continuous  current  may  be  practi- 
cally the  same  as  that  offered  to  an  alternating  current ;  that 
is,  that  the  resistance  and  impedance  shall  be  nearly  alike,  and 
the  small  number  of  turns  thus  allowed  must  be  of  coarse  low- 
resistance  wire,  in  order  to  carry  without  overheating  the 
amount  of  current  necessary  to  supply  a  field  of  the  requisite 
strength.  If  the  self-induction  of  the  instrument  is  not  made 
negligible,  the  less  resistance  encountered  by  direct  current 
would  allow  of  a  current  flow  greater  than  that  caused  by  a 
source  of  alternating  E.M.F.,  and  the  instrument  would  read 
higher  on  direct  than  on  alternating  current  for  the  same 
voltage. 

ELECTROMAGNETIC    VOLTMETERS. 

Here  again,  as  in  many  preceding  instruments,  we  find  that 
the  only  difference  between  the  voltmeter  and  the  ammeter  is 
that  the  former  is  wound  with  many  turns  of  fine  wire  instead 
of  a  few  of  coarse  wire.  The  internal  mechanism  of  an  electro- 


204       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


magnetic  voltmeter  of  the  solenoid  type  is  shown  in  Fig.  157. 
Obviously,  in  the  case  of  the  magnetic  vane  form,  the  same 
substitution  of  fine  for  coarse  wire  is  of  itself  sufficient  to  effect 
the  conversion  of  the  instrument. 

Where  electromagnetic  voltmeters  are  to  be  used  for  general 
test  work,  and  it  is  ^desired  that  their  indications  shall  remain 
correct  independent  of  the  frequency  of  the  circuit  on  which 
measurement  is  being  made,  the  number  of  turns  in  the  station- 

ary spool  must,  as 
already  explained,  be 
made  a  minimum  in 
order  that  the  self- 
induction  may  be  as 
small  as  possible.  In 
order  to  reduce  this 
value  to  a  poinl  where 
the  difference  between 
the  resistance  and  im- 
pedance is  practically 
zero,  the  resistance 
must  be  made  so  low 
that  if  a  good  fraction 
of  the  maximum  po- 
tential for  which  the 
apparatus  is  designed 
is  applied  to  it 
for  any  considerable 

period,  the  heat  generated  will  change  the  resistance,  and 
hence  the  accuracy  of  the  indications,  because,  as  stated  in 
the  opening  remarks  of  this  chapter,  the  accuracy  of  the  indi- 
cations of  a  voltmeter  depends  upon  the  assumption  that  the 
R  of  the  instrument  is  constant.  For  portable  instruments 
of  this  class,  therefore,  that  must  be  correct  on  any  frequency 
and  on  direct  current  as  well,  low-resistance  windings  are 
employed,  and  it  is  necessary  to  observe  care  that  the  meter  be 
attached  to  the  circuit  for  only  brief  periods  in  order  that  its 
heating  may  not  introduce  appreciable  errors.  They  are  usually 
provided  with  spring-actuated  contact  keys,  so  that  current 
will  not  flow  through  them  unless  the  key  is  intentionally 
depressed,  and  then  only  as  long  as  it  is  kept  depressed. 


J57. 


MEASUREMENT  OF  POTENTIALS.  205 

Where  such  instruments  are  not  intended  for  all-around 
work,  but  are  of  the  switchboard  pattern,  to  be  used  in  connec- 
tion with  one  installation  only,  the  frequency  of  the  current 
delivered  by  that  installation  is  ascertained  in  advance  and  the 
instrument  calibrated  to  be  correct  for  that  frequency.  Com- 
paratively high  self-induction  is  in  this  case  permissible,  which 
enables  the  use  of  enough  wire  to  make  the  resistance  sufficiently 
high  to  keep  the  current  flowing  down  to  a  value  which  will 
not  introduce  heating  errors. 

To  boil  the  above  down,  portable  alternating  current  voltme- 
ters of  the  dynamometer  and  electromagnetic  types  are  accurate 
on  varying  frequencies  only  by  sacrificing  their  resistance  and 
by  sacrificing  the  possibility  of  leaving  them  continuously  in 
circuit  without  heating  error ;  switchboard  instruments  of  either 
type  may  be  left  continuously  in  circuit  and  are  of  higher  re- 
sistance, but  are  accurate  only  on  the  particular  frequency  for 
which  they  are  calibrated. 

HOT-WIKE    VOLTMETERS. 

It  is  not  necessary  to  go  into  the  details  of  these,  for,  as  in 
the  case  of  the  electromagnetic  instruments  above,  they  differ 
from  the  hot-wire  ammeters  only  in  that  the  resistance  of  the 
wires  is  made  as  high  as  possible  in  order  to  consume  a  minimum 
amount  of  current,  and  in  having  auxiliary  resistances  coupled 
in  series  with  the  thermal  wires  in  order  to  adjust  the  calibra- 
tion instead  of  having  shunts  coupled  across  the  terminals. 

INDUCTION    VOLTMETERS. 

Here  again  we  have  merely  high-resistance  ammeters  calibrated 
to  show  potentials.  The  description  of  the  former  instruments 
covers  these  fully. 


COMPENSATED  VOLTMETERS. 

Where  a  voltmeter  is  used  in  a  central  station,  the  ordinary 
type  gives  merely  the  potential  at  the  station  bus-bars  and 
conveys  no  idea  of  the  voltage  at  the  centers  of  distribution, 
the  latter  varying  with  the  load  on  the  lines.  It  is  important 
that  the  potential  at  the  distribution  centers  be  known  at 


206       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

the  station,  as  the  primary  object  of  the  station  regulation 
is  to  maintain  the  potential  at  the  lamps  as  nearly  constant 
as  possible,  the  station  voltage  being  of  secondary  interest 
only.  It  is,  of  course,  possible  to  run  a  pair  of  small  wires 
whose  resistance  is  low  as  compared  with  that  of  the  volt- 
meter, back  from  the  distribution  centers  to  the  station  and 
to  attach  an  ordinary  voltmeter  to  them  in  order  to  ascertain 
this  factor.  Such  an  expedient  is,  however,  costly,  and  in  con- 
sequence various  efforts  have  been  made  to  design  potential 
indicators  which  Avill  show  the  distribution  center  voltage  with- 
out necessitating  these  return  or  "  pilot "  wires. 

One  form  of  these  compensated  voltmeters  is  shown  in  Fig. 
158.     This   is    an  instrument  of  the  permanent  magnet   type 


FIG.  158. 

suitable  for  direct  currents  only,  and  has  its  movable  coil  double 
wound ;  one  of  the  windings  is  a  regular  voltmeter  winding, 
and  if  the  other  is  disconnected  causes  the  instrument  to  read 
volts  in  the  ordinary  way.  The  other  winding  is  like  that  of  an 
ammeter  and  receives  its  current  because  of  the  potential  applied 
by  the  drop  across  a  shunt  connected  in  the  outgoing  circuit. 
The  electrical  connections  are  made  so  that  the  effort  of  the 
latter  opposes  that  of  the  voltmeter  winding.  When,  therefore, 
no  current  is  flowing  through  the  line  the  instrument  indicates 
the  station  potential.  When  current  is  being  drawn,  the  drop 
across  the  shunt  causes  the  deflection  of  the  instrument  needle 
to  be  less  than  that  due  to  the  station  potential  by  an  amount 
dependent  on  the  strength  of  the  current.  The  adjustment 
is  so  made  that  this  diminution  is  the  same  as  the  drop  along 
the  supply  line  to  the  center  of  distribution  with  a  given  current 


MEASUREMENT  OF  POTENTIALS. 


207 


flow,  and  the  apparatus  thus  indicates  the  potential  at  the 
distribution  center  without  necessitating  the  employment  of 
"  pilot "  wires. 

A  similar  expedient  is  employed  in  the  case  of  alternating 
current  apparatus,  the  plan  being  as  indicated  in  Fig.  159. 
Here  the  voltmeter  is  connected  to  the  terminals  of  one  of  the 
windings  of  a  voltmeter  transformer,  the  primary  coil  of  the 
same  being  connected  across  the  line.  The  transformer  has  a 


Load 


Gen. 


FIG.  159. 


third  winding  of  a  few  turns  of  heavy  conductor,  through 
which  the  outgoing  current  must  flow,  and  which  is  so  con- 
nected that  its  tendency  is  to  decrease  the  secondary  E.M.F. 
induced  by  the  primary  winding.  In  commercial  transformers 
of  this  type,  leads  are  tapped  out  from  the  windings  and  termi- 
nate in  contact  buttons  so  that  the  degree  of  compensation  may 
be  varied  to  suit  the  conditions  of  various  installations.  A 
compensating  voltmeter  transformer  of  this  kind  is  shown  in 
Fig.  160. 

SUPPRESSED  SCALE  VOLTMETERS. 

In  ordinary  central  station  practice  the  range  of  voltage  to 
be  covered  by  the  station  voltmeter  is  very  small.  For  in- 
stance, in  a  plant  running  normally  at  110  volts,  an  instrument 


208 


ELECTRIC  AND   MAGNETIC  MEASUREMENTS. 


whose  lowest  indication  is  100  volts  and  the  highest  120  volts 
serves  all  practical  purposes.  If  the  same  length  of  scale  can 
be  included  between  these  two  points  as  that  included  between 
the  zero  and  full  scale  markings  of  an  ordinary  voltmeter  cover- 
ing all  values  intermediate  between  zero  and  125  volts,  the 
width  of  each  scale  division  representing  a  volt  is  evidently  over 
five  times  as  great,  and  voltage  determinations  may  be  made  with 
that  much  higher  accuracy.  The  station  attendant  also  may 
stand  much  farther  away  from  his  instrument  and  still  be  able 
to  read  the  voltage  with  the  same  exactitude. 

Instruments  having  such  scales  are  called  "  suppressed  scale 
voltmeters,"  or  sometimes  "potential  indicators,"  and  the 
method  of  attaining  the  end  is  as  follows : 

In  the  case  of  direct-current  instruments  of  the  movable  coil 
spring  opposed  type  the  springs  are  wound  up  by  turning  their 
abutments  until  they  have  a  sufficient  tension  to  make  it  neces- 
sary to  apply  the  desired  minimum  voltage  before  the  needle 

can  start  to  move  across  the  scale. 
If  no  change  other  than  this  were 
made,  the  value  per  division  repre- 
senting a  volt  would  be  no  greater 
than  in  the  original  device.  If, 
however,  the  resistance  in  circuit 
with  the  moving  coil  is  cut  down 
to  say  one  half  the  original  amount 
the  current  flowing  through  the 
coil  will  obviously  be  doubled,  and 
this  would  cause  it  to  move 
twice  the  distance  against  the 
unchanged  spring  tension  as  the 
coil  in  the  original  apparatus. 
If,  further,  the  number  of  turns 
forming  the  moving  coil  is  dou- 
bled, the  doubled  number  of 
times  that  the  current  flows  through  the  field  coil  will  cause  a 
doubled  deflectional  effort.  By  combining  these  two  expedients 
it  is  perfectly  possible  to  attain  five  or  for  the  matter  of  that  ten 
times  the  torque  used  in  a  meter  having  divisions  running  from 
zero  on  upward,  and  thus  to  attain  the  desired  end  of  having  the 
value  per  division  one  fifth  or  one  tenth  as  great.  A  permanent 


FIG.  160. 


MEASUREMENT  OF  POTENTIALS.  209 

magnet-moving  coil  instrument  of  this  suppressed  scale  pattern 
is  illustrated  in  Fig.  161. 

Where  the  voltmeter  is  of  the  electromagnetic  type,  and  the 
opposing  force  is  supplied  by  a  weight  on  which  gravitational 
attraction  exerts  a  stronger  and  stronger  pull  as  the  angle  of 
deflection  of  the  needle  increases,  the  expedient  of  winding  up 
springs  can  of  course  not  be  used.  The  plan  then  employed  is 
to  provide  a  loose  weight  which  rests  on  a  fixed  shelf  when  no 
current  is  on  the  instrument,  but 
which  is  lifted  by  the  instru- 
ment plunger  as  soon  as  this 
starts  to  rise  a  very  small  amount. 
The  weight  thus  added  is  large 
enough  to  prevent  the  needle 
from  moving  further,  until  a 
higher  predetermined  voltage  is 
attained,  whereupon  the  weight 
and  the  plunger  rise  together  as 
in  the  ordinary  apparatus.  The 
added  deflection  per  volt  im-  FlG  161 

pressed   is  obtained  by  increas- 
ing   the  number  of    turns  in  the  stationary  current  carrying 
spool  and  decreasing  the  resistance  of  that  circuit  precisely  as 
in  the  case  of  the  permanent  magnet  apparatus. 


CALIBRATION     OF    VOLTMETERS. 

It  is  of  course  possible  to  calibrate  a  voltmeter  by  using  a 
known  standard  resistance  and  passing  through  it  a  known  cur- 
rent, the  resulting  potential  difference  between  the  resistance 
terminals  being  calculated  from  Ohm's  law.  The  value  of  the 
current  strength  may  be  obtained  by  the  voltameter  method,  if 
desired,  and  that  of  the  resistance  by  any  of  the  absolute  methods 
mentioned  in  Chapters  II  and  IV.  Such  a  method  of  establishing 
potentials  is,  however,  cumbersome,  and  moreover  complicated 
by  the  fact  that  the  voltage-reading  device  is  ordinarily  of  itself 
of  finite  resistance  and  will  therefore  modify  the  potential  at  the 
terminals  of  the  standard  resistance  when  connected  in  parallel 
therewith.  The  error  may  be  allowed  for  by  simple  arithmet- 


210       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

ical  calculation,  but  of  course  involves  the  accurate  determina- 
tion of  the  resistance  of  the  voltmeter. 

A  better  and  much  more  simple  method  of  voltmeter  calibra- 
tion consists  in  comparing  the  indications  of  the  instrument  with 
the  E.M.F.  of  a  standard  cell  by  the  aid  of  the  already  much  men- 
tioned potentiometer.  If  two  cells  made  at  different  times  and 
preferably  one  of  the  Clark  and  the  other  of  the  Weston  type 
are  used  for  the  standards,  and  these  are  found  to  agree  with  one 
another,  it  is  morally  certain  that  the  results  obtained  are  of  an 
accuracy  limited  only  by  the  accuracy  of  adjustment  of  the 
potentiometer  and  the  closeness  with  which  the  instrument  indi- 
cations are  observed. 

Station  Potentiometers. 

The  ordinary  potentiometer  capable  of  measuring  ever^y  volt- 
age up  to  its  maximum  capacity  is  rather  an  expensive  piece  of 
apparatus  and  seldom  available  in  commercial  installations. 
By  restricting  the  number  of  values  that  the  instrument  will 
show  to  two  or  three,  however,  choosing  them  so  that  they  approx- 
imate closely  those  at  which  the  station  instruments  are  usually 
run,  the  apparatus  is  considerably  simplified  and  much  reduced 
in  price.  A  simple  potentiometer  for  the  calibration  of  station 
voltmeters  made  along  the  lines  indicated  is  illustrated  in  Fig. 
162.  The  resistance  MN  is  provided  with  terminals  at  three 
points  only,  so  that  while  but  three  resistance  coils  only  are 
needed,  three  potentials  can  be  compared.  Three  standard  cells, 
iS',  are  provided,  and  there  are  flexible  terminals,  CO,  so  arranged 
that  any  one  or  any  combination  of  them  may  be  connected  at 
will.  When  but  one  cell  is  in  circuit,  the  galvanometer  inserted 
in  the  standard  cell  line  will  show  no  deflection  when  there  is 
60  volts  difference  of  potential  between  M  and  P,  120  volts 
between  M  and  0,  or  240  volts  between  M  and  N.  If  two  cells 
are  used,  these  values  are  of  course  doubled,  and  if  all  three, 
trebled.  By  these  means  the  apparatus  is  to  a  certain  extent 
self-checking  as  far  as  the  E.M.F.  of  the  standard  batteries  is 
concerned,  because  if  with  a  fixed  potential  between  M  and  0 
no  deflection  is  obtained,  with  one  cell  in  circuit  and  when  the 
same  potential  is  applied  to  the  circuit  between  TkTand  P  and 
two  cells  are  used  there  is  also  no  deflection,  it  is  morally  cer- 
tain that  both  of  the  standard  cells  are  in  proper  condition,  and 


MEASUREMENT  OF  POTENTIALS. 


211 


that  the  resistance  wire  of  the  potentiometer  has  suffered  no  de- 
terioration. A  resistance  R  of  about  10,000  ohms  value  is  in- 
serted in  the  cell  circuit,  so  that  no  detrimental  current  can  flow 
and  momentarily  affect  the  cell  accuracy  even  if  the  potential 
applied  to  the  potentiometer  resistance  terminals  differs  widely 


120 


«e~-      60     —. >j 

^AAY^AAAAAAAA<MAAAAAAAAAAAAO-AAAAAAAAAAAAA<) 
P  0  ^ 


r 


FIG.  162. 

from  the  normal.  A  short-circuiting  key,  H,  is  arranged  so 
that  this  resistance  may  be  cut  out  as  soon  as  it  is  apparent 
that  balance  is  nearly  attained  in  order  to  utilize  the  full  sensi- 
bility of  the  outfit. 

In  this  station  potentiometer  it  is  necessary  to  vary  the  applied 
E.M.F.  until  balance  is  attained  as  indicated  by  the  absence  of 
a  galvanometer  deflection  instead  of  moving  the  galvanometer 
contact  along  the  potentiometer  wire.  The  voltmeter  that  is  to 
be  calibrated  is  therefore  connected  with  its  one  terminal  to  the 
wire  M  and  the  other  to  N,  0,  or  P,  according  to  the  value  de- 


212      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

sired,  and  the  applied  E.M.F.  varied  by  a  resistance  A  in  the  sup- 
ply line  until  balance  is  reached.  As  in  the  majority  of  stations 
the  working  potential  is  either  nearly  120  or  nearly  240  volts, 
and  the  fact  that  the  working  voltmeter  is  accurate  on  these 
potentials  need  alone  be  established,  this  simple  instrument 
answers  practically  all  station  requirements. 


The  Wheatstone  Bridge  for  Calibrating  Voltmeters. 

If  a  standard  cell  and  a  galvanometer  of  moderate  sensibility 
are  available,  the  ordinary  Wheatstone  bridge  may  be  used  to 
advantage  in  checking  the  calibration  of  voltmeters.      The  pro- 
cedure involves  as  a  first  step  the  measurement  of  the  resist- 
ance of  the  yolt- 
meter   as   closely 
as  possible,  using 
the  bridge  in  the 
s—ss"        )  ordinary  way  for 

i  -^  '  -i  -  -  1        - "» ~~-?-t---~  -  -/•/»  i  - 

The  apparatus  is 

then  connected 
up  as  shown  in 
Fig.  163.  To  take 
a  concrete  case, 
suppose  the  volt- 
meter to  be  of  150  volts  range  and  that  its  resistance  has 
been  determined  as  15,000  ohms.  The  source  of  E.M.F. 
supplies  150  volts,  or  over,  and  the  standard  cell  gives 
1.019  volts.  The  error  of  the  voltmeter  when  100  volts 
difference  of  potential  exists  at  its  terminals  is  desired.  Evi- 
dently, with  100  volts  at  the  voltmeter  terminals,  there  will 
flow  through  its  15,000  ohms  of  resistance  a  current  of 
_|.o  o.^  _  .006667  amperes.  In  order  that  this  same  current, 
which  necessarily  flows  through  the  bridge  also,  may  cause  a 
difference  of  potential  equal  to  the  standard  cell  voltage  at 
the  bridge  terminals,  plugs  must  be  withdrawn  to  insert 

=  152.8  4-  ohms  at  that  point.       The  ordinary  bridge 


FIG.  163. 


—  — 
.00667 

has  no 


ohm  coils,  and  the  best  approximation  that  can  be 


MEASUREMENT  OF  POTENTIALS.  213 

made  will  therefore  be  153   ohms.      Figuring  backward   from 
this  point  we  find  that  -^W-  =    .00666    amperes     must    flow 


through  this  to  cause  the  drop  to  equal  the  standard  cell  volt- 
age, and  that  this  current  causes  a  drop  of  .00666  x  15,000  = 
99.9  volts  across  the  voltmeter  terminals.  The  voltmeter 
needle  should  therefore  indicate  99.9  volts  when  the  regulating 
rheostat  in  the  supply  circuit  has  brought  the  current  strength 
to  a  point  such  that  the  galvanometer  shows  no  deflection  when 
the  key  in  its  circuit  is  closed,  and  if  it  does  not,  the  difference 
is  the  error  at  that  point. 

Similar  checks  may  be  made  at  any  point  on  the  scale. 

In  practice,  the  bridge  resistance  that  has  been  calculated  is 
first  plugged  in  and  the  rheostat  manipulated  until  the  volt- 
meter  indicates  approximately  the  right  potential.  The  key  in 
the  standard  cell  circuit  is  then  momentarily  depressed,  and  if 
deflection  of  the  galvanometer  ensues  the  rheostat  is  further 
varied  until  this  is  no  longer  the  case.  The  voltmeter  is  then 
read  and  the  error,  if  any,  noted. 

The  above  method  gives  a  means  of  checking  voltmeters  to  a 
degree  of  accuracy  amply  high  for  the  most  refined  station 
practice,  and  has  the  great  advantage  of  requiring,  in  addition 
to  the  instruments  that  are  usually  on  hand  anyway  for  other 
work,  only  an  inexpensive  standard  cell. 

Some  manufacturers  of  Wheatstone  bridges  equip  them  so 
that  they  may  be  used  to  measure  E.M.F.'s  as  in  an  ordinary 
potentiometer.  The  plan  has,  however,  nothing  to  recommend 
it  as  against  the  method  just  described,  and  calls  for  more 
auxiliary  apparatus. 

Calibration  of  Alternating  Current  Voltmeters. 

In  the  case  of  alternating  current  voltmeters  it  is  scarcely 
possible  to  go  back  directly  to  fundamental  standards,  as  is  done 
with  direct  current  instruments.  The  calibration  is,  however, 
only  slightly  more  difficult  in  that  all  that  is  necessary  is  to 
calibrate  on  direct  current  by  one  of  the  methods  described,  a 
voltmeter  which  will  indicate  the  same  on  either  direct  or 
alternating  potentials  of  like  value,  such,  for  instance,  as  a  hot- 
wire pattern  indicating  voltmeter  o$  the  Kelvin  volt  balance, 


214        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

and  then  use  it  as  a  standard  for  comparing  the  meter  under 
test.  If  at  the  expiration  of  such  test  the  sub-standard  is  again 
checked  on  direct  current  and  found  to  have  its  calibration 
unchanged,  the  results  may  safely  be  accepted  as  correct. 

Of  course  an  electrostatic  voltmeter  of  the  Kelvin  multi- 
cellular  or  any  other  convenient  type  may  be  used  as  a  transfer 
instrument  in  a  similar  way.  If,  however,  the  potentials  in- 
volved are  small,  it  must  be  remembered  that  a  correction  has 
then  to  be  applied  to  compensate  for  the  effect  of  the  potential 
difference  set  up  by  the  contact  between  the  dissimilar  metals 
comprising  the  suspension  and  the  moving  vanes  respectively, 
as  already  described. 


CHAPTER  VIII. 


MEASUREMENT   OF   POWER. 

THE  power  expended  in  any  electrical  circuit  is  measured  by 
the  summation  of  the  products  of  the  effective  current  value  and 
the  effective  difference  of  potential  at  each  instant.  With  direct 
currents  the  power  is  therefore  simply  the  product  of  the  cur- 
rent in  amperes  and  the  potential  in  volts,  the  watt  being  the 
name  given  to  the  unit  product. 

When  measuring  power  in  an  alternating  current  circuit,  how- 
ever, the  simple  arithmetical  product  of  effective  volts,  as  shown 
by  the  voltmeter,  and 


E 


0 


E 


FIG.  164. 


effective  amperes,  as 
shown  by  the  amme- 
ter, no  longer  gives 
the  true  power  in 
watts.  This  is  because 
nearly  every  circuit 
possesses  either  in- 
ductance or  capacity, 
which  causes  the  cur- 
rent to  reach  a  maximum  some  time  later  than  or  in  advance 
of  the  maximum  value  of  E.M.F.  At  any  instant,  therefore, 
the  actual  power  is  the  product  of  the  simultaneously  exist- 
ing momentary  values  of  the  voltage  and  current,  and  the 
mean  of  the  sum  of  all  of  these  products  is  different  from 
the  product  of  the  effective  voltage  by  the  effective  current, 
as  will  be  evident  without  entering  into  a  mathematical 
discussion,  by  simple  reference  to  Figs.  164,  165,  166,  and 
167.  In  Fig.  164  the  status  of  affairs  with  direct  current 
is  shown,  the  height  a  b  of  the  line  J,  I  above  the  horizontal  axis 
being  drawn  to  a  scale  representing  the  current  strength  and 
the  height  a  c  in  a  similar  manner  the  value  of  the  potential. 
The  time  is  laid  out  along  the  horizontal  axis,  so  that,  the 
current  being  continuous  and  steady,  the  lines  /,  /  and  E>  E  are, 

215 


216       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

of  course,  straight  and  parallel  to  the  axis.  It  is  evident  that 
whatever  instant  is  chosen,  the  product  of  a  b  and  a  c  remains 
the  same.  The  case  of  alternating  current  is  shown  in  the  suc- 
ceeding figure.  Here  the  horizontal  axis  0  0  again  represents 
time,  the  curve,  /,  7,  the  values  of  the  current  at  any  instant, 
and  JE,  E,  the  potential  values  at  any  instant.  The  reversal  of 
current  direction  is  indicated  by  drawing  the  curves  below  the 
horizontal  axis  for  such  length  of  time  as  they  are  opposite  to 
the  initial  direction.  If  the  circuit  is  non-inductive  and  without 
capacity,  the  current  varies  with  and  in  phase  with  the 
potential,  and  the  curves  therefore  have  the  relative  position 
shown  in  Fig.  165.  In  such  circuits  the  effective  watts  can  be 


FIG.  165. 

calculated  by  simply  multiplying  together  the  effective  volts  and 
effective  amperes.  If,  however,  the  circuit  is  inductive,  the 
current  no  longer  varies  in  phase  with  the  voltage,  but  its 
changes  in  value  lag  behind  it,  the  relative  position  of  the  two 
being  dependent  on  the  relative  value  of  the  inductance.  Fig. 
166  shows  the  current  and  potential  curves  under  these  circum- 
stances. Here  it  is  evident  that  the  product  of  the  effective 
volts  shown  by  the  voltmeter  and  the  effective  amperes  shown 
by  the  ammeter  no  longer  gives  the  effective  watts.  Take,  for 
instance,  the  point  a  on  the  time  line.  Here  the  current  has 
the  value  indicated  by  the  height  of  the  ordinate  a  c,  but  the 
potential  value  at  that  instant  is  zero,  so  that  their  product  is 
zero.  The  maximum  product  at  any  period  is  no  longer  the 
product  of  the  maximum  values  of  the  current  and  voltage  but 
that  at  some  instant,  n,  where  neither  is  it  at  its  maximum.  As 


MEASUREMENT  OF  POWER. 


217 


algebraic  signs  must  be  taken  into  consideration,  we  might,  theo- 
retically, even  arrive  at  the  case  given  in  Fig.  167,  where  the 
potential  and  current  curves  are  in  opposing  phases  throughout, 
so  that  their  product  is  zero,  although  the  voltmeter  would  show 


FIG.  166. 


the  normal  effective  voltage  and  the  ammeter  the  normal  effects 
ive  amperage. 

The  measurement  of  the  displacement  between  current  curves 
is  by  no  means  easy,  and  even  if  it  were  it  would  be  necessary 


FIG.  167. 


to  make  calculations  to  determine  energy  from  volt  and  ampere 
readings  with  alternating  current  on  an  inductive  circuit. 
Fortunately  there  are  available  means  of  constructing  instru- 
ments which  will  give  the  watts  direct  without  this  necessity. 


218       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


DYNAMOMETER    WATTMETERS. 

The  Siemens  ammeter  described  on  page  165  may  be  con- 
verted into  an  instrument  that  will  measure  the  watts  in  any 
circuit  by  constructing  the  stationary 'coil  of  comparatively  few 
turns  of  large  diameter  wire  connected  so  that  all  of  the  current 
to  be  measured  flows  through  it,  and  making  the  movable  coil  of 
many  turns  of  fine  wire  with  its  terminals  connected  directly, 
or  through  the  interposition  of  a  resistance,  across  the  line  like 
a  voltmeter.  When  this  is  done  the  field  set  up  by  the  station- 
ary coil  is  evidently  proportionate  to  the  effective  amperage, 
and  that  by  the  fine  wire  coil  to  the  effective  E.M.F.  If  the 
current  and  voltage  do  not  attain  their  maximum  values  simul- 
taneously, that  is  to  say,  if  they  are  out  of  phase  with  one 
another,  the  reaction  between  the  two  fields  will  diminish*  with 
increasing  phase  difference,  and  the  instrument  indications  will 
be  true  watts  instead  of  volt  amperes. 

THE   WATT   BALANCE. 

The  Kelvin  balance  described  on  page  18  may  likewise 
be  utilized  as  a  wattmeter  if  one  of  the  sets  of  coils  is  made 
to  carry  the  total  current  flowing  and  the  other  is  connected 
across  the  line,  so  that  the  current  through  it,  and  hence  the 
magnetic  field  that  it  sets  up,  is  proportional  to  the  voltage. 
As  in  the  case  of  the  dynamometer  wattmeter,  the  fine  wire  or 
"  potential  winding  "  is  used  for  the  movable  coils,  as  the  current 
to  be  carried  to  them  through  the  suspending  ligaments  is  then 
very  much  less. 

WHITNEY   WATTMETER. 

This  is  an  instrument  whose  principle  is  the  same  as  that  of 
the  dynamometer  wattmeter,  but  the  construction  is  modified  to 
make  the  apparatus  portable  and  hence  more  suitable  for  com- 
mercial measurements.  As  can  be  seen  from  Fig.  168,  the 
heavy  current  winding  is  formed  of  two  coils  supported  on 
suitable  frames,  which  inclose  instead  of  being  inclosed  by  the 
fine  wire  coil.  The  latter  is  mounted  on  a  shaft  with  pointed 
ends  resting  in  jeweled  bearings,  and  the  spring  effort  which 


MEASUREMENT   OF   POWER. 


219 


balances  the  turning  effort  of  the  coil,  when  the  button  pro- 
jecting through  the  top  of  the  instrument  case  is  rotated,  is 
that  of  a  pair  of  volute  springs  of  flat  strip  phosphor-bronze, 
instead  of  a  spirally  wound  round  wire.  The  current  is  led 
into  and  out  of  the  movable  coil  through  the  volute  springs, 
so  that  the  mercury  cups  used  in  the  Siemens  form  are 
done  away  with.  The  scale  over  which  the  needle  attached 
to  the  torsion  button  moves  is  divided  so  as  to  indicate  watts 
directly  instead  of  degrees  from  which  the  watts  must  be  calcu- 
lated by  referring  to  tables  or  curves.  The  needle  that  is 


FIG.  168. 

attached  to  the  shaft  carrying  the  potential  coil,  and  which  is 
brought  back  to  a  reference  mark  on  the  dial  by  turning  the 
torque  button  to  obtain  a  reading,  is  allowed  a  somewhat 
greater  range  of  movement  than  the  corresponding  needle  in 
the  Siemens  form.  A  short  scale  is  drawn  on  both  sides  of  the 
reference  mark,  so  that  the  instrument  can  be  used  to  read  watt- 
ages  differing  slightly  from  those  indicated  by  the  needle 
attached  to  the  torsion  head.  For  instance,  if  the  torsion  head 
needle  was  pointing  to  the  50  watt  division  with  a  given  cur- 
rent flowing,  but  the  other  or  zero  needle  was  pointing,  not  to 
the  reference  mark,  but  to  the  division  to  the  left  thereof  corre- 


220       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


spending  to  10  watts  value,  the  true  reading  is  60  watts,  as 
the  divisions  of  the  short  scale  are  so  spaced  that  it  would  be 
necessary  to  turn  the  torsion  head  until  its  attached  needle 
pointed  to  60  watts  on  the  principal  scale  in  order  to  bring  the 
zero  needle  to  its  zero  line.  Similarly  if  the  zero  needle  pointed 
to  the  10  watt  mark  at  the  right  of  the  reference  line,  the  true 
reading  would  be  40  watts. 

The    short    scale    is    convenient    in   lamp    testing,    as  the 

torsion  needle  may  be 
set  to  the  average 
wattage  that  the  lamps 
are  supposed  to  take, 
and  the  amount  in  ex- 
cess of  or  less  than 
this  may  be  read*  off  at 
once  from  the  short 
scale.  A  better  idea  of 
the  scale  and  general 
appearance  of  such  an 
instrument  may  be  had 
from  Fig.  169. 

WESTON  WATTMETERS. 

A  still  further  modi- 
fication of  the  Siemens 
wattmeter  is  the  Wes- 
ton  instrument  shown 
in  perspective  in  Fig. 
170  and  diagrammati- 
cally  in  Fig.  171.  Here 
the  heavy  wire  coil  is 

likewise  stationary  and  surrounds  the  circular  potential  coil,  the 
latter  being  supported  on  steel  pivots  resting  in  jeweled  bear- 
ings and  having  the  current  lead  to  and  from  it  through  volute 
springs.  However,  no  torsion  head  is  used,  and  the  potential 
coil,  instead  of  being  maintained  at  practically  the  same  position 
for  every  value  within  the  capacity  of  the  apparatus,  rotates 
about  its  axis  over  an  angle  of  about  eighty  degrees.  As  in  the 
case  of  the  spring  controlled  voltmeters  and  ammeters,  the 
opposing  force  that  increases  in  proportion  to  the  deflection  of 


FIG.  169. 


MEASUREMENT  OF  POWER. 


221 


.    FIG.  170. 


the  needle  is  supplied  by  the  volute  springs,  so  that,  as  the 
reaction  between  the  currents  in  the  two  coils  is  nearly  directly 
proportional  to  the  watts, 
the  scale  divisions  are 
nearly  equally  spaced. 

This  form  of  instru- 
ment has  an  advantage 
over  the  dynamometer 
types,  in  that  no  manip- 
ulation is  necessary  and 
the  needle  points  at  once 
to  the  scale  mark  show- 
ing the  watts.  On  the 
other  hand,  as  the  angle 
between  the  planes  of 
the  current  and  potential 
coils  is  variable,  the  mu- 
tual induction  between  the  two  varies  with  different  positions  of 
the  needle.  For  any  given  difference  in  phase  between  the 
potential  and  current  the  apparatus  may  have  its  scale  divisions 

drawn  so  that  the 
indications  are  cor- 
rect. If,  however, 
the  power  factor 
varies,  this  varying 
mutual  induction  in- 
troduces an  error  that 
cannot  be  compen- 
sated for,  and  can  be 
allowed  for  only 
when  the  phase  dif- 
ference is  known. 

The  error  from 
this  source  is  mini- 
mized by  making  the 
mutual  inductance  of 
the  windings  as  small  as  possible,  and  with  proper  design 
can  be  made  negligible  for  much  commercial  work  where  the 
power  factors  do  not  cover  too  wide  a  range.  However,  it 
is  not  safe  to  assume  that  such  an  instrument  will  give  correct 


FIG.  171. 


222     ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


indications  when  making  measurements  on  both  unity  and  very 
low  power  factors,  such  as  an  incandescent  lamp  load  and  the 
energy  consumed  by  the  primary  winding  of  an  open  secondary 
circuit  transformer,  for  instance,  as  with  the  best  design  there 
will  be  a  difference  in  accuracy  of  at  least  two  or  three  per  cent 
under  such  circumstances. 

INDUCTION  WATTMETERS. 

A  wattmeter  suitable  for  the  measurement  of  watts  on  alter- 
nating current  circuits  only,  may  be  made  following  along  the 

lines  of  an  induction 
motor.  Referring  to 
Fig.  172,  if  D  is  a  disk 
of  good  conducting 
metal,  such  as  aluminum 
or  copper,  and  BAB  a 
series  of  sheet-iron 
stampings  assembled  to- 
gether and  surrounded 
on  the  B  extensions  with 
fine  wire  windings  and 
on  the  A  extension  by  a 
coarse  wire  winding,  and 
these  coils  are  connected 
in  circuit  like  the  fine 
and  coarse  coils  of  a 
dynamometer  watt- 
meter, the  disk  will  be 
subjected  to  a  torque  pro- 
portional to  the  watts 

flowing.  Briefly,  the  reason  for  this  is  that  the  alternate 
ing  current  through  the  coarse  winding  produces  currents 
in  the  disk  whose  paths  are  as  shown  by  the  concentric 
circles  in  the  figure  and  of  a  strength  proportional  to  the  cur- 
rent. The  current  flowing  through  the  fine  wire  coils  sets  up  a 
magnetic  flux  in  the  legs  B,  B,  whose  strength  is  proportional  to 
the  E.M.F.,  and  the  reaction  between  this  and  the  current  in  the 
disk  urges  the  latter  to  rotate  with  a  torque  proportional  to  the 
product  of  the  current  and  the  potential,  i.e.,  the  watts.  The 
magnetic  circuit  for  the  lines  of  force  flowing  is  made  of  less 


FIG.  172. 


MEASUREMENT  OF  POWER. 


223 


reluctance  by  the  addition  of  the  set  of  stampings  C  placed 
below  the  disk. 

Having  thus  an  apparatus  in  which  an  element  is  urged  to 
rotate  with  a  torque  proportionate  to  the  watts,  all  that  is 
necessary  to  convert  it  into  an  indicating  wattmeter  is  the 
attachment  of  an  index  to  the  disk  D,  a  calibrated  scale 
over  which  this  needle  may 
swing,  and  a  spring  for  oppos- 
ing the  disk  torque. 

The  indications  of  the 
needle  of  induction  instru- 
ments are  usually  dampened 
or  made  "  dead  beat "  by 
adding  a  permanent  magnet 
between  whose  polar  extrem- 
ities the  conducting  disk 
rotates,  the  resultant  eddy 
currents  supplying  the  neces- 
sary retardation. 

The  Westinghouse  indicat-  FIG.  173. 

ing    induction  wattmeter    is 

shown  in  Fig.  173.  The  conducting  disk  here  takes  the  form 
of  a  cylinder,  but  the  principle  being  the  same  as  that  of 
the  above  wattmeter,  the  operation  may  be  readily  under- 
stood without  going  into  further  details. 


HOT   WIRE   WATTMETER. 

A  simple  and  ingenious  wattmeter  utilizing  the  expansion  of 
wires  heated  by  the  passage  of  current  and  proposed  by  Bauch 
is  diagrammatically  illustrated  in  Fig.  175.  Here  a  and  b  are  the 
two  hot  wires,  S  being  a  shunt  inserted  in  one  current  carrying 
conductor,  and  c  a  resistance  inserted  between  the  junction  of 
the  two  wires  and  the  other  conductor.  Starting  from  the 
assumption  that  the  elongation  of  a  heated  wire  is  proportionate 
to  the  heat  that  it  is  called  upon  to  dissipate,  it  can  be  shown 
(see  ^Industrie  Eleetrique,  Sept.  10,  1901)  that  the  difference 
between  the  elongation  of  two  wires  interconnected  as  shown  in 
Fig.  175  is  proportional  to  the  watts  dissipated  in  the  circuit 
L,L. 


224       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


A  mechanical  arrangement  for  indicating  the  difference  in 
the  elongation,  and  hence  pull  of  the  two  wires,  is  shown  in 
Fig.  176.  Here  c  and  /  are  solid  levers,  d  and  e  flexible  liga- 


B        S 


FIG.  175. 


ments  taking  the  place  of  pivots,  and  h  an  arm  with  a  bifurcated 
end  for  actuating  the  needle  as  in  the  hot  wire  volt  and    am- 


Resistance 


'hunt 


Generator 


FIG.  176. 


meters  described  on  p.  178.  When  a  difference  of  potential 
exists  between  k  and  /,  but  no  current  flows  through  the  shunt, 
the  wires  a  and  b  are  heated  alike,  as  the  resistance  of  the  shunt 


MEASUREMENT   OF  POWER. 


225 


is  negligible  as  compared  with  the  rest  of  the  circuit  so  formed. 
The  lever  h  will  therefore  move  vertically  only  and  fail  to  rotate 
the  needle.  A  similar  reasoning  applies  when  current  flows 
through  the  shunt,  but  there  is  no  difference  of  potential  between 
k  arid  I.  If  there  is  both  a  difference  of  potential  and  a  current 
flow  through  the  shunt,  b  is  heated  more  than  a,  the  lever  / 
rocks,  and  the  arm  h  urges  the  needle  up  the  scale.  Its  excur- 
sions are  proportionate  to  the  watts. 

CONNECTIONS  OF  WATTMETERS. 

The  way  in  which  the  current  and  potential  coils  of  the 
dynamometer  type  wattmeters  and  their  equivalents  are  con- 
nected in  circuit  has  a  considerable  influence  on  the  accuracy 
of  the  results  obtained.  Such  connections  may  be  made  in 


FIG.  177 


FIG.  178. 


either  of  the  two  ways  indicated  by  Figs.  177  and  178  respec- 
tively. In  the  former,  the  potential  coil  is  connected  across  the 
terminals  of  the  circuit  whose  watt  consumption  is  to  be 
measured,  the  current  coil  being  cut  in  before  it ;  whereas,  in 
the  second  case,  the  potential  coil  is  across  the  supply  line  and 
the  current  coil  inserted  further  on.  With  the  first  arrange- 
ment the  current  flowing  through  the  series  winding  is  evidently 
that  demanded  by  the  load  and  by  the  potential  coil,  and  in  the 
second  case,  while  the  current  is  that  demanded  by  the  load 
alone,  the  potential  indicated  is  not  that  at  the  load  terminals 
but  that  due  to  the  drop  across  the  currenkconsuming  apparatus 
plus  that  across  the  current  winding. 

To  see  the  effect  of  these  two  plans  it  will  be  instructive  to 
take  an  actual  example  in  each  case.  Considering  first  the 
results  with  connections  as  in  Fig.  177,  let  the  load  be  a  16  C.  P. 
incandescent  lamp,  and  the  potential  of  the  supply  mains  120 


226       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

volts ;  assume  also  that  the  resistance  of  the  potential  coil  E  is 
4,000  ohms.  The  current  through  the  lamp  may  be  taken  as 
.5  amperes  and  that  through  the  potential  coil  £$-$•$  =  .03 
amperes.  The  current  demanded  by  the  potential  winding  and 
which  passes  through  the  current  coil  is  therefore  six  per  cent 
of  the  current  required  by  the  lamp,  and  the  instrument  indica- 
tions are  that  percentage  higher  than  the  wattage  expended  in 
the  lamp  alone.  Such  an  error  is,  of  course,  entirely  too  great 
even  for  the  roughest  commercial  work. 

If  the  connections  are  as  in  Fig.  178,  the  results  would  be  as 
follows :  The  current  flowing  through  the  series  coil  is  now 
only  that  demanded  by  the  lamp,  but  the  potential  applied  to  the 


FIG.  179. 


lamp  is  less  than  the  120  volt  line  potential  by  the  amount  of 
the  drop  across  the  series  winding.  Let  the  resistance  of  the 
latter  be  taken  as  .2  ohms,  a  fair  value.  With  one  half  ampere 
flowing,  the  drop  is  therefore  .1  volts,  and  as  the  instrument 
takes  account  of  the  line  voltage  only,  the  resultant  indications 
are  less  than  one  tenth  of  a  per  cent  high. 

This  error  is  less  than  in  the  preceding  case,  but  if  the  cur- 
rent demanded  is  large  and  approximating  the  maximum 
capacity  of  the  series  winding,  and  the  potential  applied  is  low, 
it  also  may  become  appreciable,  although  seldom  as  great  as  in 
the  first  case.  For  accurate  work -it -is  therefore  necessary 
that  the  resistance  of  both  windings  of  the  instrument  be  known 
in  order  that  proper  corrections  may  be  applied  to  the  results 


MEASUREMENT  OF  POWER. 


227 


obtained.  In  almost  all  cases  it  is  desirable  to  use  the  second 
scheme  of  connections. 

COMPENSATED  WATTMETERS. 

If  certain  connections  of  a  wattmeter  are  made  permanently 
inside  of  the  case,  so  that  it  is  assured  that  the  circuits  will  be 
as  in  Fig.  177,  the  error  due  to  the  current  drawn  by  the 
potential  coil  can  be  compensated  for  in  a  simple  manner. 
Referring  to  Fig.  179,  which  shows  diagrammatically  the  internal 
connections  of  a  wattmeter  and  the  way  in  which  it  is  attached 
to  the  line,  it  can  be  seen  that  in  addition  to  the  regular  potential 
coil  and  the  non-  + 
inductive  resistance 
placed  in  series  there- 
with to  adjust  the 
calibration,  turns  of 
wire  convey  the  po- 
tential circuit  cur- 
rent around  the  spool 
carrying  the  series 
coil.  The  number 
of  these  turns  is 
made  equal  to  the 
number  of  turns  in  __ 

the  movable  coil,  the    

result  being  that  the 

additional  fixed  coil  field  due  to  the  additional  current  flowing 
through  it  demanded  by  the  potential  winding  is  exactly  neu- 
tralized by  the  back  turns  of  the  same  current  carried  around 
the  same  number  of  times  through  this  compensating  winding. 
An  instrument  so  equipped  will  therefore  indicate  the  watts 
expended  on  the  receiving  circuit  without  requiring  the  appli- 
cation of  any  correction  factor. 

THKEE-VOLTMETER    METHOD. 

The  watts  expended  in  any  given  circuit  may  be  determined 
by  using  three  voltmeters  or  making  three  successive  measure- 
ments with  one  voltmeter  in  accordance  with  the  following 
plan:  Referring  to  Fig.  180,72  is  a  non-inductive  resistance 
connected  in  series  with  the  inductive  resistance  included 


JL_±. 


FiG.  180. 


228       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


between  b  and  o  in  which  the  power  to  be  measured  is  expended. 
Three  voltmeters  are  then  attached,  one  to  show  the  potential 
between  a  and  5,  another  that  between  b  and  c,  and  the  third 
that  across  the  line  ac.  It  is  not  within  the  scope  of  this  volume 
to  give  a  demonstration  of  the  correctness  of  the  conclusion, 
but  it  is  a  fact  that  the  watts  in  be  are,  under  these  circum- 

stances,   represented    by   the 

formula 


2E 

To  obtain  maximum  accuracy, 
R  should  be  chosen  so  that 
the  potential  across  it  is  as 
nearly  as  possible  equal  to  the 
difference  in  potential  between 
the  terminals  of  be.  As  R 
is  in  series  with  be,  and  the 
drop  across  it  should  be  practi- 
cally the  same,  it  is  evident 
that  this  method  of  testing 
calls  for  the  presence  of  a 
testing  voltage  double  that 
demanded  for  the  normal  oper- 
ation of  the  device  inserted 
between  b  and  <?.' 

THREE-AMMETER    METHOD. 

Three  ammeters  may  be 
used  to  measure  the  watts  ex- 
pended  in  any  given  circuit  in 
a  similar  way.  In  this  case  the 

connections  are  made  as  in  Fig.  181,  0  being,  as  before,  the  circuit 
whose  consumption  is  to  be  determined.  Connected  in  parallel 
to  C  is  a  non-inductive  resistance  R,  and  three  ammeters  indi- 
cating the  currents  through  R,  0  and  R  4-  0  are  inserted  as 
shown.  Under  these  conditions  the  watt  expenditure  in  C  is 

given  by  the  formula 
T-> 

—  -  (T  *  —  7"  2  —  T  ?\ 
2  v  3          i          2  )• 

In   contradistinction  to  the  three-voltmeter  method,  the  three- 


FrG  181 


MEASUREMENT   OF  POWER.  229 

ammeter  one  does  not  call  for  an  increased  potential  for  testing 
purposes,  but  it  does  demand  increased  current.  On  the  other 
hand,  while  with  the  three-voltmeter  method  it  is  possible  to 
arrange  a  switch  by  means  of  which  connections  may  be  rapidly 
shifted  so  that  one  voltmeter  may  be  used  for  reading  all  three 
potentials,  a  similar  plan  is  not  practicable  with  the  ammeters, 
owing  to  the  heavy  currents  involved  and  the  necessity  of 
keeping  the  circuits  intact  and  their  resistances  unchanged,  so 
that  three  meters  are  essential. 

Both  the  three-voltmeter  and  the  three-ammeter  methods  have 
the  very  serious  drawback  that  a  very  small  percentage  error  in 
the  accuracy  of  the  indications  or  the  observations  of  the  indi- 
cations of  any  of  the  instruments  introduces  a  very  large  error 
in  the  results.  Neither  is  used  in  modern  practice  unless  it 
becomes  absolutely  necessary  to  make  a  test  when  voltmeters  or 
ammeters  alone  are  available,  and  every  precaution  is  then  ex- 
ercised to  have  the  readings  as  exact  as  possible. 


POWER    CONSUMPTION   OF   MULTIPHASE   CIRCUITS. 

The  various  instruments  for  and  methods  of  watt  measurement 
above  described  are  all  suitable  only  for  use  on  simple  direct  or 
alternating  current  circuits  involving  two  conductors  only. 
Where  the  case  involves  multiphase  currents  the  conditions 
become  essentially  different. 

If  the  line  on  which  measurement  is  to  be  made  is  a  four- 
wire  two-phase  one,  watts  are  measured  just  as  one  would 
measure  them  in  two  independent  alternating  current  circuits,  a 
separate  wattmeter  being  used  in  the  conventional  way  with 
each,  and  their  indications  arithmetically  added.  With  three- 
phase  three-wire  systems  two  wattmeters  must  likewise  be  em- 
ployed if  the  results  are  to  be  accurate,  whether  the  loads  on  the 
different  phases  are  like  or  unlike.  These  instruments  are  to 
be  connected  in  the  circuits,  as  in  Fig.  182,  the  current  coil  of  one 
being  inserted  in  one  line,  the  same  coil  of  the  other  in  another 
line,  and  the  potential  coils  of  each  bridged  across  between  their 
respective  lines  and  the  third  conductor.  The  sketch  shows 
the  connections  of  the  receiving  apparatus  as  being  in  delta,  but 
the  connections  of  the  wattmeter  are  made  the  same  if  they  are 


230       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

arranged  in  Y.  The  total  watts  absorbed  is  given  by  the 
algebraic  sum  of  the  indications  of  the  two  wattmeters.  When 
the  power  factor  of  the  load  is  over  50  per  cent  the  algebraic 
sum  is  the  arithmetical  one,  but  when  less  than  50  per 
cent  it  is  the  arithmetical  difference,  so  that  the  indications 
of  the  lower  reading  wattmeter  must  be  subtracted  from  the 
higher  reading  one  to  get  the  correct  result. 

It  is  essential  that  the  potential  coil  connections  be  made  as 
in  Fig.  182,  as  otherwise  the  results  obtained  may  be  erroneous. 
This  caution  is  necessary  because  approximately  the  same  poten- 


FiG.  182. 

* 

tial  difference  exists  between  a  and  b  as  between  a  and  <?,  and 
the  potential  terminals  of  the  wattmeters  of  the  b  and  a  phases  are 
therefore  sometimes  connected  by  careless  manipulatora  to  the 
a  and  b  ones  respectively,  instead  of  to  c.  The  magnitude  of 
the  error  thus  introduced  can  be  understood  from  the  following 
example  :  Referring  to  Fig.  183,  assume  that  the  power  factor 
of  the  delta-connected  load  shown  is  unity,  but  that  the  load  is 
unbalanced,  the  current  in  the  three  phases  being  10,  20,  and  30 
amperes  respectively,  as  indicated.  Being  of  unity  power  factor, 
the  total  current  consumption  with  100  volts  difference  of 
potential  between  each  of  the  three  conductors  is  evidently 
1,000  +  2,000  +  3,000  =  6,000  watts.  A  wattmeter  inserted 


MEASUREMENT  OF  POWER.  231 

at  a,  and  having  its  potential  coil  connected  from  a  to  5,  would 
indicate  2,500  watts,  arid  one  inserted  at  c  with  its  potential  coil 
between  c  and  £,  3,500  watts,  the  sum  of  these  being  6,000,  as 
above.  If  it  were  attempted  to  obtain  the  results  by  using  the 
wattmeter  a  alone,  and  transferring  its  free  terminal  first  to  b 
and  then  to  c,  the  sum  of  the  readings  would  be  2,500  +  2,000 
=  4,500  only.  The  demonstration  of  these  facts  is  simple,  and 
can  be  found  on  page  947,  of  Volume  XL,  of  the  Electrical 


100V 


200V    - 4 100V  - 


20  Amp. 


AAA/WVV 


^r-  -VVVVVVV-  ~NJ 

Cf  30  Amp  \\ 


FIG.  183. 

World  and  Engineer,  in  an  article  by  McAllister,  from  which 
the  above  example  has  been  taken. 

CALIBRATION   OF   WATTMETERS. 

The  calibration  of  a  wattmeter  for  direct  currents  involves 
nothing  more  than  using  an  ammeter  in  series  with  the  current 
coil  and  a  voltmeter  connected  to  the  same  points  as  the  poten- 
tial coil  of  the  wattmeter.  The  product  of  volts  and  amperes 
as  thus  indicated  is  the  true  wattage.  In  this  measurement  it 
is  necessary  to  reverse  the  direction  of  the  current  through  the 
wattmeter,  as  in  such  instruments  the  magnetic  fields  are  much 


232      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

less  powerful  than  in  the  majority  of  direct  current  meters,  and 
stray  fields  may  introduce  appreciable  errors  which  are,  of 
course,  eliminated  by  making  two  readings  with  the  reversed 
current  and  accepting  their  mean  as  the  true  instrument  in- 
dication. 

Calibration  on  alternating  current  is  a  far  more  difficult 
matter  if  sure  results  are  to  be  had.  A  dynamometer  ammeter, 
an  ampere  balance,  or  a  hot  wire  ammeter  may  be  used  for 
measuring  the  current,  and  the  corresponding  instruments 
wound  with  fine  wire  or  an  electrostatic  voltmeter,  for  measur- 
ing the  potential.  The  product  of  the  volts  and  amperes  in 
this  case  will,  however,  give  the  watts  only  if  the  load  being 
measured  is  non-inductive.  For  commercial  accuracy  a  bank 
of  incandescent  lamps  is  sufficiently  near  to  being  absolutely 
non-inductive,  although  resistance  wires  doubled  back  on^them- 
selves  are  better.  If  the  load  is  not  non-inductive  it  becomes 
necessary  to  measure  the  difference  in  phase  between  the  cur- 
rent and  the  potential  curves,  using  one  of  the  methods  de- 
scribed in  Chapter  X,  and  then  to  calculate  the  watts  from  the 
cosine  of  the  angle  of  phase  difference  and  the  indication  of 
the  alternating  current  voltmeter  and  ammeter. 

Another  way  is  to  use  as  a  secondary  standard  a  wattmeter 
that  has  been  calibrated  on  direct  current  and  of  which  it  is 
known  from  the  design  and  construction  that  no  errors  are  in- 
troduced with  inductive  loads.  The  Kelvin  balance  and  the 
dynamometer  wattmeter  as  usually  made,  answer  this  require- 
ment for  all  practical  purposes  at  reasonably  high  power 
factors,  and  it  is  safe  to  assume  that  if  they  show  up  correct  on 
a  direct  current  test  with  reversed  connections,  they  will  be 
correct  on  alternating  current  also.  The  only  fault  that  may 
enter  to  upset  this  conclusion  is  the  development  of  a  partial 
short  circuit  in  one  of  the  instrument  windings,  but  with 
apparatus  that  has  been  tested  for  a  reasonable  period,  such 
fault  would  have  its  presence  clearly  indicated  by  a  change  in 
calibration,  even  if  it  were  not  sufficiently  serious  to  make  its 
presence  evident  by  the  heating  of  the  short-circuited  convolu- 
tions when  alternating  current  was  passed. 

In  the  few  existing  wattmeters  designed  for  indicating 
directly  the  input  into  a  multiphase  system  of  conductors,  the 
test  is  made  by  checking  each  of  the  pairs  of  potential  and 


MEASUREMENT  OF  POWER.  233 

current  windings  separately,  such  apparatus  being  nothing  but 
two  wattmeters  with  the  movable  coils  mechanically  joined,  so 
that  the  needle  indicates  directly  the  sum  of  the  efforts,  instead 
of  having  two  needles  whose  readings  must  be  added  arith- 
metically. 


CHAPTER   IX. 

MEASUREMENT  OF  CAPACITY 
ABSOLUTE    METHODS. 

Air   Condensers. 

IN  Chapter  II,  page  33,  there  was  described  a  standard  air 
condenser  devised  by  Lord  Kelvin.  The  capacity  of  such  a 
piece  of  apparatus  can  be  figured  directly  from  its  geometrical 
dimensions,  and  the  known  specific  inductive  capacity  of  air. 
The  errors  that  may  creep  into  the  geometric  measurements 
are,  however,  appreciable,  and  the  apparatus  itself  is  bulky  and 
seldom  available,  so  that  it  is  more  common  to  obtain  the  true 
value  of  the  capacity  of  any  condenser  from  absolute  units  (in 
contradistinction  to  comparison  methods)  by  the  plan  follow- 
ing : 

Absolute    Capacity   Measurement  with   Galvanometer. 

The  throw  of  the  coil  of  a  ballistic  galvanometer  gives  the 
capacity  of  the  apparatus  from  which  the  charge  causing  the 
throw  was  delivered  if  certain  characteristics  of  the  galvanometer 
are  known. 

In  the  first  place,  the  galvanometer  constant  must  be  deter- 
mined. To  do  this,  a  low  potential  source  of  current,  preferably 
a  storage  battery,  is  used,  across  whose  terminals  is  connected  a 
resistance  of  about  1,000  ohms  value.  In  shunt  to  a  fraction  of 
this  resistance,  say  2  ohms,  there  is  connected  the  galvanom- 
eter, and  the  resultant  deflection  observed  after  the  instrument 
has  settled  down.  If  E  is  the  E.M.F.  of  the  battery,  R  the 
resistance  of  the  galvanometer,  d^  the  observed  deflection,  and 
E^  the  potential  at  the  galvanometer  terminals  (in  this  case 


K  =  .002),  the  constant  is     - 

i 
The  period  of  vibration  of  the  movable  element  of  the  galva- 

nometer must  next  be  determined.  This  is  done  by  setting  it 
swinging  in  any  suitable  way,  such  as  by  passing  a  current 
momentarily,  and  then  observing  carefully  the  time  required  for 

234 


MEASUREMENT   OF  CAPACITY. 


235 


it  to  make,  say,  ten  to  twenty  swings.  By  swings  are  meant 
double  oscillations  from  zero  to  a  maximum  in  one  direction 
back  through  zero  to  a  maximum  in  the  opposite  direction,  and 
to  zero  again.  The  number  of  swings  divided  by  the  time  in 
seconds  gives  the  time  of  vibration  T. 

The  third  determination  is  that  of  the  decrement  due  to  the 
damping  of  the  motion  caused  by  the  molecular  friction  of  the  sus- 
pending fiber,  and  of  the  air  currents  that  the  coil  must  set  in 
motion.  The  decrement  is  the  ratio  of  the  amplitude  of  any 
vibration  to  the  amplitude  of  the  vibration  next  succeeding.  To 


FIG.  184. 

obtain  this  the  moving  element  of  the  galvanometer  is  set  in 
vibration,  and  the  amplitude  of,  say,  the  first  and  tenth  vibra- 
tions observed.  If  the  first  excursion  of  the  galvanometer  index 
was,  say,  forty  divisions,  and  the  tenth,  one  division,  the  decre- 
ment would  evidently  be  1.04.  Call  the  Napierian  logarithm  of 
decrement,  X. 

With  these  characteristics  determined,  the  condenser  to  be 
measured,  the  galvanometer,  battery,  and  a  resistance  box  are 
connected  up  as  shown  in  Fig.  184.  On  depressing  the  key 
shown  in  the  figure,  the  condenser  becomes  charged  by  the 
known  fraction  of  the  battery  E.M.F.  determined  by  the  ratio 
of  the  resistance  included  between  the  condenser  terminals, 


236         ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

ab  and  the  box  resistance  cd.  When  the  key  is  raised  the  con- 
denser discharges  through  the  galvanometer,  causing  it  to  make 
a  deflection  d^. 

The    quantity  of  electricity  discharged  by  the  condenser  is 
then  calculable  from  the  equation 

K  T 

Q=jd*d*x^: 


If  the  condenser  capacity  is  F  and  the  potential  of  the  source 
that  charged  it,  E^  we  have,  as  Q  =  FE^,  F  =  Q  -j-  E2.  Sub- 
stituting in  the  above  formula,  we  have 


In  this,  as  in  all  capacity  measurements  involving  the  use  of 
a  ballistic  galvanometer,  care  must  be  taken  to  see  that  the 
period  of  a  complete  swing  of  the  instrument  is  sufficiently  long, 
as  the  hypothesis  on  which  the  equation  rests  is  that  the  inertia 
of  the  moving  system  is  great  enough  to  allow  of  the  complete 
discharge  of  the  condenser  through  the  galvanometer  winding 
before  the  deflection  has  had  time  to  attain  sensible  magnitude. 

COMPARISON    METHODS. 

Once  having  a  standard  of  capacity  as  determined  by  the 
above  methods,  there  are  several  plans  of  measuring  unknown 

capacities  in  terms  thereof. 
Before  turning  to  them,  mention 
may  be  made  of  convenient 
forms  of  the  standard. 

In  Chapter  II  the  use  of  air 
as  the  dielectric  in  standard  con- 
densers was  instanced    by  the 
Kelvin  instrument,  and  the  use 
ih      of  mica  also  described.     Paper, 
I     while     inferior     to     mica     for 
FIG.  185.  condenser  construction,  is  some- 

times employed  in  rough  work, 

but  then  must  be  not  only  dipped  in  very  hot  melted  paraffine 
before  being  built  up,  but  the  condenser  as  a  whole  should,  after 


MEASUREMENT  OF  CAPACITY. 


237 


completion,  be  entirely  immersed  in  the  same  compound,  and 
allowed  to  cool  with  the  cake  surrounding  it  in  order  to  exclude 
the  air. 

While  for  very  closely  adjusted  standards  a  single  condenser 
provided  with  a  short-circuiting  plug,  as  shown  in  Fig.  185,  is 

/  m.  £  each.,  J  m.f.  each. 


Capacity  crs  shown, 
2.4  m.f 

FIG.  186. 


\ H 


commonly  employed  for  measurements  of  commercial  accuracy, 
it  is  desirable  that  the  standard  capacity  be  subdivided  into 
units  which  can  be  grouped  together  as  desired. 

This  may  be  done  by  mounting  a  number  of  individual  con- 


;;;     '.•  :•"  '•"••' ^ 


Fro.  187. 

densers  in  a  common  case,  and  leading  the  conductors  attached 
to  their  terminals  to  a  series  of  contact  buttons  over  which  a 
movable  plate  may  be  swept.  From  Fig.  186  it  may  be  seen 
that  by  moving  these  plates  so  as  to  rest  on  one  or  more  buttons, 
the  one  or  more  attached  condensers  are  coupled  in  parallel, 


238      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


and,  in  the  particular  apparatus  illustrated,  a  range  of  from 
.1  to  10  microfarads  in  .1  microfarad  steps  becomes  obtain- 
able. A  perspective  of  this  adjustable  condenser  is  given  in 
Fig.  187. 

An  older  but  still  common  form  of  standard  condenser  has 
the  various  individual  condensers  of  which  it  is  built  assembled 
in  one  case  and  connected  together  by  movable  tapered  plugs 


.05 


.05 


B 


D 


E 


.05 


.05 


2 


.5 


FIG.  188.  v 

like  those  in  resistance  boxes.  Fig.  188  gives  the  diagram  of 
the  connections  of  one  of  these,  Fig.  189  being  an  illustration 
of  the  complete  apparatus.  When  condensers  of  the  individual 
capacities  indicated  by  these  figures  are  used,  it  is  evidently 

possible  by  insert- 
ing plugs  so  as  to 
couple  the  various 
combinations  to- 
gether in  parallel,  to 
obtain  any  capacity 
between  .05  and  1 
microfarad  in  steps 
of "  .05  microfarad. 
Care  must  be  taken 
that  plugs  are  not 
FIG.  189.  placed  in  the  recep- 

tacles   of    opposite 

ends  of  a  single  bar,  A,  B,  C,  etc.,  as  if  so  the  condenser  is  short 
circuited,  and  any  battery  used  to  charge  it  would  be  short  cir- 
cuited also. 

This  kind  of  a  condenser  has  the  advantage  that  it  is  possible 
to  self-check  it  to  a  certain  extent,  as  the  .05  microfarads  may 
be  compared  with  one  another,  and  the  .5  with  the  other  four 
connected  in  parallel. 


MEASUREMENT  OF  CAPACITY. 


239 


Capacity  by  Direct  Deflection. 

As  the  deflections  of  a  ballistic  galvanometer  are  proportional 
to  the  quantity  of  electricity  passed  through  it,  the  capacity  of 
an  unknown  condenser  may  readily  be  determined  when  one  of  a 
known  capacity  is  also  available  by  first  charging  the  known 
condenser  from  a  certain  source  of  E.M.F.  and  then  discharging 
it  through  the  galvanometer,  noting  the  ensuing  deflection,  after 
which  the  operation  is  repeated  with  the  unknown  condenser  in 
place  of  the  standard  one.  The  galvanometer  deflections  are  then 
in  the  ratio  of  the  capacities.  The  times  during  which  the  po- 


K 


FIG.  190. 


tential  is  applied  to  both  condensers  must  be  the  same,  say  five 
seconds,  and  it  is  necessary  to  take  the  mean  of  several  read- 
ings to  allow  for  small  variations  in  this  period.  It  is  also 
necessary,  for  the  best  accuracy,  that  the  standard  be  selected 
so  that  its  capacity  is  as  nearly  as  possible  that  of  the  unknown 
condenser ;  the  whole  method  is  at  best,  however,  a  rough  one. 

Divided   Charge  Method. 

For  this,  connections  are  made  between  a  ballistic  galvanom- 
eter 6r,  a  standard  condenser  F^  the  unknown  condenser 
F2J  a  double  contact  key  K,  and  a  charging  battery  with  its 
key,  all  as  shown  in  Fig.  190.  With  the  apparatus  so  arranged, 
the  battery  key  is  depressed  so  that  the  standard  condenser  Fl 


240      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

is  charged,  and  the  key  kept  closed  for  an  observed  number  of 
seconds,  say  five.  The  battery  key  is  then  opened  and  key  K 
raised  so  that  the  standard  condenser  discharges  through  the 
galvanometer,  the  throw  thus  caused  being  noted.  Key  K 
is  then  again  opened  and  the  battery  key  closed  as  before  to 
charge  the  standard  condenser.  At  the  lapse  of  the  same  period 
as  at  first,  the  key  K  is  depressed,  which  places  the  two  con- 
densers in  parallel,  so  that  the  charge  in  the  standard  is  divided 
between  them  in  the  ratio  of  the  capacities.  This  being  accom- 
plished, the  TTkey  is  again  raised  and  the  deflection  caused  by 
the  discharge  of  the  quantity  of  current  remaining  in  the  stand- 
ard condenser  noted.  If,  then,  the  capacity  of  the  standard 
condenser  be  designated  by  Fl  and  that  of  the  unknown  by 
F%,  we  have  Fl  is  to  F2  as  D2  (the  second  deflection)  is  to 
Dl  —  Z>2,  in  which  DY  is  the  first  deflection.  For  maximum 
accuracy,  the  capacity  of  the  standard  should  be  made  as  nearly 
as  possible  equal  to  that  of  the  condenser  of  unknown  value. 

Bridge    Methods. 

Condenser  capacities  may  be  compared  when  they  are  intercon- 
nected by  a  network  of  conductors  arranged  like  those  in  the 
Wheats  tone  bridge.  This  method  has  the  same  advantage  that 
exists  in  the  measurement  of  resistances  with  a  bridge  ;  that  is, 
it  is  a  zero  one,  and  errors  due  to  reading  the  galvanometer 
deflections  are  thus  avoided.  It  is  further  possible  to  eliminate 
practically  all  errors  due  to  inductance. 

In  the  simple  bridge  method,  the  standard  condenser  Fl  and 
the  unknown  one  F2  are  connected  as  shown  in  Fig.  191 ;  ad- 
justable resistances  7^  and  R^  a  galvanometer,  a  battery  and 
a  special  contact  key,  a,  5,  being  also  employed.  When  the  a 
end  of  the  key  is  depressed  the  condensers  are  evidently  being 
charged  by  the  battery,  and  when  the  b  end  is  depressed  they 
are  being  discharged  through  the  resistances  and  the  galvanom- 
eter. To  make  the  test,  a  is  first  depressed  for  a  brief  inter- 
val and  then  raised  for  its  full  height,  so  that  the  condenser 
discharges  as  stated.  If  this  results  in  a  deflection  of  the 
galvanometer,  the  ratio  of  Rl  to  R2  is  altered  and  the  trial 
again  made,  b  being  kept  depressed  until  then,  in  order  that  the 
condensers  may  be  kept  discharged.  When  a  ratio  of  Rl  to  R2 


MEASUREMENT  OF  CAPACITY. 


241 


is  finally  attained  such  that  no  galvanometer  deflection  ensues 

r>  TT 

when  a  is  raised  and  b  depressed,  the  relation  —  =  _ 2  holds 

#2      Jf\ 

good.  This  is  so  because  if  the  galvanometer  does  not  deflect 
when  the  condensers  discharge,  the  potentials  at  its  points  of 
attachment  to  the  network  are  equal;  being  charged  by  the 
some  potential,  the  quantities  of  current  stored  by  the  con- 
densers are  proportional  to  their  capacities,  and  these  quantities 


are  in  inverse  proportion  to  the   resistances  R1  and  R2  in  the 
circuits  leading  to  them. 

In  this,  as  in  all  other  capacity  measurements  involving  the 
employment  of  adjustable  resistances,  it  is  essential  that  the 
latter  be  absolutely  without  capacity  and  without  inductance. 
Such  coils  are  purchasable  on  the  open  market,  and  are  best 
made  as  follows :  Each  resistance  unit  is  made  up  of  two  wires 
connected  in  parallel,  each  having  twice  the  resistance  of  that 
desired  for  the  coil,  and  each  of  the  two  coils  is  wound  into  a 
flat  and  very  thin  spiral.  The  two  spirals  are  placed,  theii  flat 
faces  touching  and  connected  so  that  the  currents  flowing 
through  them  run  in  opposite  directions.  Being  now  connected 
in  parallel,  the  opposing  windings  make  the  coil  non-inductive 
as  the  current  flows  in  reversed  directions  in  parallel  conductors 


242     ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

for  a  like  distance.  The  capacity  of  such  a  unit  is  negligible, 
as  it  forms  a  condenser  in  which  the  potential  between  its  two 
surfaces  is  but  half  of  that  between  the  innermost  and  the  out- 
side convolutions,  and  the  distance  between  the  surfaces  is  that 
between  the  wires  forming  these  convolutions.  Such  construc- 
tion is  necessarily  expensive,  but  must  be  employed  if  reliable 
results  are  to  be  had. 

Modified  Bridge  Method. 

•If  the  connections  in  Fig.  191  are  modified  to  those  in  Fig. 
192,  the  galvanometer  and  battery  positions  being  interchanged, 


FIG.  192. 


we  have  another  method  of  measuring  an  unknown  capacity  in 
terms  of  a  standard.  The  keys  in  the  battery  and  galvanometer 
circuits  are  manipulated  so  that  the  condensers  are  charged  by 
the  battery  and  subsequently  discharged  through  the  resistances 
and  the  galvanometer  in  a  way  analogous  to  that  in  the  preced- 
ing method.  The  values  of  the  resistances  are  likewise  to  be 
varied  until  no  galvanometer  deflection  results  when  the  con- 
densers are  unloaded  by  depressing  the  galvanometer  key, 
whereupon  the  capacity  F1  is  to  F2  as  R2  is  to  R^.  This  follows 
because  the  condensers,  connected  in  series,  must  each  contain 
a  like  quantity,  and  the  discharge  from  F^  through  R^  times  the 
potential  difference  between  the  terminals  of  Rl  must  equal  the 


MEASUREMENT  OF  CAPACITY. 


243 


discharge  through  R2  times  the  potential  difference  across  R2. 
We  therefore  have  the  relation 


.B, 


Thompson  Method  of  Mixtures. 

This  method,  so  called  because  it  involves  mixing  the  opposed 
charges  of  two  condensers  so  as  to  determine  whether  or  not 


J     t 


^^aAr^ 


FIG.  193. 


they  are  equal,  is  an  acknowledged  standard,  particularly  for 
the  measurement  of  cable  capacities,  and  is  also  a  favorite  when 
the  capacity  of  one  condenser  is  to  be  accurately  determined  in 
terms  of  that  of  another. 

In  making  it,  connections  are  arranged  as  in  Fig.  193.  In 
making  a  test,  the  two  center  buttons  of  the  special  key  L  are 
first  depressed  so  that  the  condensers  are  charged  by  means  of 
the  battery  with  the  potential  differences  that  exist  between  the 
terminals  of  the  resistances  R}  and  R2.  After  this  has  been 
done  the  keys  are  released,  making  contact  with  c  and  d  respec- 
tively, which  places  the  two  condensers  in  parallel  and  allows 


244        ELECTRIC  AND   MAGNETIC  MEASUREMENTS. 

the  charges  to  mix.  If  these  charges  were  equal  and  opposite 
when  the  key  E  is  depressed,  there  will  be  no  galvanometer 
deflection,  as  there  is  no  current  to  cause  it.  If  there  should 
be  a  deflection,  the  charges  were  not  alike,  and  the  resistances 
R1  and  R2  must  therefore  be  varied  until  this  condition  is 
attained.  When  it  is,  the  ratio  Ft  is  to  F2  as  R2  is  to  R1  evi- 
dently holds.  When  the  capacity  of  a  cable  is  being  measured, 
the  point  of  junction  of  the  resistances  Rl  and  R2  must  be 
connected  to  earth,  as  the  earth  forms  the  one  coating  of  each 
condenser. 

If  the  results  obtained  are  to  be  comparable  with  others,  some 
standard  time  of  charging  must  be  used,  which  time  may  con- 
veniently be  chosen  as  five  seconds.  The  value  of  the  capacities 


FIG.  194. 

should  also  be  as  nearly  alike  as  possible.  The  key  L  is  a 
special  device  known  as  the  Lambert  capacity  key,  one  of  which 
is  shown  in  Fig.  194. 

CAPACITY   BY   LOSS    OF   CHARGE. 

If  the  terminals  of  a  charged  condenser  are  left  connected 
together  through  a  known  resistance,  R,  for  a  period  of  T  sec- 
onds, its  capacity  can  be  calculated  from  the  formula 

T 

F= - . 

2.303  R  (log  D!  -  log  Z>2) 

in  which  D1  is  the  deflection  of  a  ballistic  galvanometer  caused 
by  the  discharge  through  it  of  the  condenser  after  it  has  first 
been  electrified  and  before  the  resistance  is  attached,  and  D2 
the  same  after  it  has  been  freshly  electrified  and  then  left  dis- 


MEASUREMENT  OF   CAPACITY.  245 

charging  through  the  resistance  R  for  T  seconds.  If  R,  the 
resistance,  is  in  megohms,  the  capacity,  F,  is  in  microfarads. 

If  the  condenser  under  test  is  of  the  type  in  which  paper  is 
used  as  the  dielectric,  its  own  internal  resistance  is  frequently 
sufficiently  low  to  enable  the  above  test  to  be  made,  it  being,  of 
course,  in  that  event  necessary  to  determine  the  condenser 
resistance  by  one  of  the  methods  described  in  that  section  of 
Chapter  V  treating  of  high-resistance  measurements.  If  the 
condenser  is  of  the  mica-insulated  type,  its  resistance  is  or- 
dinarily too  high  to  allow  of  this,  and  an  external  resistance  of 
20  or  30  megohms  must  be  connected  across  its  terminals. 

A  modification  of  this  test  is  made  by  connecting  up  the 
condenser,  battery,  galvanometer,  resistance  coil,  and  key,  as 


K 


FIG.  195. 

shown  in  Fig.  195.  With  the  apparatus  so  arranged  the  key 
is  depressed  and  the  steady  deflection  of  the  galvanometer 
noted.  The  key  is  then  raised  and  the  deflection  given  read 
after  the  expiration  of  T  seconds.  If  the  initial  deflection  is 
designated  by  D^  and  the  subsequent  one  by  _Z>2  the  capacity 
may  be  calculated  by  the  same  formula  given  above. 

In  both  the  foregoing,  if  the  condenser  resistance  is  inter- 
mediate between  the  low  value  which  allows  of  its  use  as  the 
resistance  through  which  the  charge  is  dissipated  and  the  high 
value  which  makes  its  figure  so  high  as  compared  to  the  one 
connected  to  its  terminals  that  the  current  flow  througl  it  is 
negligible,  the  value  of  R  in  the  formula  must  be  calculated 
from  the  law  of  divided  circuits,  page  94,  the  true  resistance 
being  that  of  the  external  one  and  that  of  the  condenser  con- 
nected in  parallel. 


246      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


CONDENSER    ABSORPTION. 

The  majority  of  types  of  condensers  have,  to  a  greater  or  less 
degree,  a  property  of  their  dielectric  by  virtue  of  which  they 
will  receive  a  quantity  of  electricity  in  excess  of  that  due  to 
their  electrostatic  capacity.  This  excess  charge  is  taken  up 
more  slowly  than  the  condenser  charge  proper,  and  the  phe- 
nomenon, known  as  condenser  absorption,  must  be  allowed  for 
in  all  capacity  measurements. 

The  absorption  of  a  given  condenser  may  be  measured  as 
follows :  A  condenser,  F^  whose  absorption  is  to  be  measured, 
is  connected  up  with  a  standard  condenser,  F^  and  resistances 
and  a  galvanometer,  all  as  shown  in  Fig.  192.  A  balance  is 
obtained  in  the  same  way  that  is  employed  in  measuring 
capacity,  but  when  obtained,  it  does  not  indicate  that  Fl  \s  to  F^ 
as  R^  is  to  R^  as  a  portion  of  the  charge,  Q,  that  has  been  put  into 
F2  has  been  absorbed.  If  the  quantity  absorbed  is  designated  by 
£,  the  potential  at  jF2's  terminals  is  that  caused  by  the  charge 
Q  —  q.  To  determine  q  the  battery  key  K.^  is  "closed  and  the 
ratio  of  the  two  resistances  adjusted,  so  that  when  the  key  7T2  is 
depressed  the  galvanometer  gives  a  small  deflection.  If  .ffj  is 
then  opened  and  a  few  seconds  are  allowed  to  elapse,  a  deflec- 
tion will  be  observed  on  closing  J?T,  which  deflection  should  be 
opposite  to  the  former  one.  By  further  adjusting  the  ratio  R^ 
to  R2,  the  two  deflections  can  be  made  equal,  whereupon  q  is 
the  quantity  of  electricity  that  would  cause  either  of  the  de- 
flections. The  value  of  q  may  then  be  readily  determined  by 
the  direct  deflection  method. 


CHAPTER  X. 

MEASUREMENT  OF  INDUCTANCE. 

As  has  been  previously  noted,  inductance,  or  more  properly, 
the  coefficient  of  inductance,  may  be  either  that  of  a  given 
conductor  or  that  between  a  plurality  of  conductors.  The 
electromotive  force  set  up  in  any  circuit  because  of  its  induc- 
tance is  the  product  of  the  coefficient  of  induction  L  and  the 
rate  at  which  the  current  flowing  changes. 

If,  with  an  alternating  current  whose  intensity  and  direction 
vary  according  to  the  sine  law,  we  take  the  instant  at  which  the 
current  strength  is  a  maximum,  we  have  chosen  a  time  when 
the  strength  is  neither  increasing  nor  decreasing,  and  the  E.M.F. 
of  self-induction  is  therefore  zero.  If  the  time  is  that  at  which 
the  current  is  passing  from  a  positive  to  a  negative  sign,  the 
rate  of  current  change  is  a  maximum,  and  the  E.M.F.  of  induction 
likewise  maximum.  Analogous  conditions  hold  for  the  whole 
cycle  of  current  changes,  the  result  being  that  the  E.M.F.  caused 
by  induction  follows  the  shape  of  the  current  curve,  but  differs 
from  it  in  phase,  in  that  the  E.M.F.  is  zero  when  the  current  is 
a  maximum  and  vice  versa. 

As  the  E.M.F.  so  set  up  opposes  any  change  in  the  E.M.F.  that 
causes  the  energizing  current  to  flow,  a  lesser  current  will 
evidently  pass  through  a  given  inductive  circuit  if  the  current 
is  alternating,  that  is,  constantly  changing  in  value  and 
direction,  than  if  it  is  direct  and  has  a  constant  value  and 
direction.  The  resistance  in  the  latter  event  is  a  purely  ohmic 
one  which  may  be  measured  by  any  of  the  methods  described  in 
Chapter  V.  The  resistance  to  the  flow  of  an  alternating 
current  may  likewise  be  measured  by  observing  the  amount  of 
current  that  is  passing  and  simultaneously  reading  the  drop 
across  the  coil  terminals  by  means  of  a  static  voltmeter.  With 
this  value  and  the  true  ohmic  resistance  known,  the  induction 
can  be  calculated,  as  is  evident  from  the  following : 

As  by  Ohm's  law,  the  E.M.F.  causing  the  flow  of  current 
through  an  ohmic  resistance  must  change  with  any  current 

247 


248    ELECTRIC   AND  MAGNETIC  MEASUREMENTS. 

change,  the  E.M.F.  and  current  for  this  component  of  the  total 
resistance  or  "  impedance  "  offered  by  the  coil  are  in  phase.  On 
the  other  hand,  as  above  explained,  the  E.M.F.  due  to  the  induc- 
tance of  the  circuit  is  a  maximum  when  the  current  strength  is 
zero,  that  is,  it  is  one  quarter  of  a  period,  90  degrees,  or  a  right 
angle  behind  the  current.  The  effects  of  the  two  may  therefore 
be  graphically  represented  by  two  sides  of  a  right-angled  tri- 
angle, as  in  Fig.  196,  in  which  Rl  is  drawn  of  a  length  possess- 
ing the  number  of  scalar  units  equal  to  the  drop  in  E.M.F.  due  to 
the  ohmic  resistance,  and  Leo  I  to  the  same  scale  represents  the 
drop  due  to  the  inductive  resistance,  while  the  length  of  the  re- 
maining side  of  the  triangle  represents  the  total  impedance. 
R  I  may  be  determined  by  measuring  the  ohmic  resistance  with 
direct  current  flowing,  and  the  hypothenuse  of  the  triangle, 


which  is,  of  course,  equal  to 


+  L2  a)2  by  measuring  the 
current  that  passes 
when  alternating 

Lu)f  current  is  applied 
and  the  drop  across 
the  coil  terminals, 
simultaneously.  In 

j?iu.  mo.  ^ 

both  R  is  the  ohmic 

resistance,  I  the  current,  and  L  the  coefficient  of  self-induction. 
«  is  equal  to  2  TT  times  the  frequency  of  the  supply  circuit. 
The  value  of  any  two  sides  of  the  triangle  being  known, 
that  of  the  remaining  one  may  be  readily  calculated. 


INDUCTANCE   BY   THE   BRIDGE   METHOD. 

In  this  the  coil  whose  inductance  is  to  be  measured,  a  gal- 
vanometer, a  set  of  non-inductive  resistances,  a  battery,  and 
ballistic  galvanometer  are  connected  up  as  shown  in  Fig.  197. 
All  of  the  resistances  must  be  of  the  type  described  on  page  241, 
free  from  inductance  and  capacity,  and  R^  must  be  capable  of 
very  exact  adjustment  which,  if  necessary,  may  be  accomplished 
by  shunting  it  with  a  second  adjustable  resistance.  The  re- 
sistances of  the  ratio  -arms  of  the  bridge  A  and  B  are  made  alike, 
and  the  value  of  the  rheostat  arm  R}  adjusted  until  the  galva- 
nometer shows  no  deflection  when  first  the  battery  key  and  then 
the  galvanometer  key  are  closed.  Thereupon  the  galvanometer 


MEASUREMENT  OF  INDUCTANCE. 


249 


key  is  first  depressed  and  then  the  battery  key,  which  will  cause 
a  deflection  or  rather  throw  Dl  of  the  galvanometer  due  to  the 
inductance  of  &  This  deflection  is  noted.  The  value  of  \  is 
then  changed  by  a  known  amount,  and  the  steady  deflection, 
which  we  will  designate  as  Z>2  that  is  then  given  when  both 
battery  and  galvanometer  keys  are  kept  closed,  is  noted.  If 
now  the  time  of  vibration  of  the  movable  element  of  the  gal- 
vanometer determined  as  described  on  page  234,  be  called  T,  and  X 
is  the  logarithmic  decrement  of  the  instrument,  and  if  the  differ- 


FlG.  197. 


ence  between  the  initial  and  final  values  of  Hl  is  r,  the    induc- 
tance can  be  calculated  from  the  equation 


In  the  above,  D^  is  the  galvanometer  throw  first  observed,  and 
D  the  second  one  noted  under  like  conditions. 


MAXWELL  S   METHOD. 

In  this  the  inductance  is  found  by  comparison  with  the 
capacity  of  a  standard  condenser.  Connections  are  made  as 
shown  in  Fig.  198,  in  which  Q  is  the  inductive  coil  anu  S  a 
standard  condenser.  The  resistances  in  the  arms  /*,  7?,  and  S 
must  be  without  inductance  and  without  capacity.  To  make  a 
measurement,  the  value  of  P  is  first  varied  until  the  galva- 
nometer shows  no  deflection  with  the  battery  key  and  its  own 


250       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

key  kept  closed.  The  battery  circuit  is  then  made  and  broken, 
whereupon  it  will  be  found  as  a  rule  that  the  galvanometer 
gives  a  throw  each  time. 

The  resistance  R  is  then  varied  until  the  battery  circuit  may 
be  interrupted  without  producing  a  galvanometer  throw,  and 
the  key  again  closed  and  held  in  order  to  see  whether  there  is 
any  steady  deflection  of  the  galvanometer  needle.  If  there  is, 
the  process  must  be  repeated  until  such  values  of  P  and  R  are 
reached  that  there  is  no  galvanometer  deflection  under  either 


FIG.  198. 


condition.     The  value  of  the  inductance  is  then  found  from 
the  equation 

or     L=QRC. 


Modified  Maxwell  Method. 

In  this  method,  proposed  by  Russell  (see  London  Electrician, 
May  4,  1894),  the  connections  are  the  same  as  in  the  original 
Maxwell  one,  but  the  condenser  8  is  of  the  adjustable  pattern, 
by  means  of  which  varying  known  capacities  may  be  inserted. 
P  is  varied  so  that  the  galvanometer  shows  no  deflection  with 
a  steady  current  flowing,  and  the  battery  circuit  is  then  made 
and  broken  with  its  key  in  the  regular  way.  If  the  condenser 


MEASUREMENT  OF  INDUCTANCE. 


251 


is  now  attached  and  its  value  varied,  it  will  be  possible  to  find 
two  values  of  condenser  capacities,  the  one  of  which  will  give 
a  throw  in  one  direction  on  opening  or  closing  the  battery  circuit 
and  the  other  in  the  reverse  direction.  By  interpolation  be- 
tween the  extent  of  these  throws  we  can  calculate  the  value  of 
the  capacity  which  would  reduce  the  deflection  to  zero.  Call- 
ing this  value  (7,  the  inductance  L  may  be  calculated  from  the 
formula  L  =  QRC. 

COMPAEISON    METHODS. 

The  value   of  an  unknown   inductance    may  be  determined 
in  terms  of  a  known  one  by  using  the  connections  and  apparatus 


FIG.  199. 

shown  in  Fig.  199.  In  this  the  galvanometer  need  not  be 
of  the  ballistic  pattern.  /S\  is  the  known  coil,  and  Sz  the  one 
whose  inductance  is  to  be  measured.  Auxiliary  resistances,  Rl  and 
R2,  are  connected  in  series  with  each,  and  these  groups  are  inter- 
connected with  other  resistances,  a  battery  and  a  battery  key,  a 
galvanometer  and  a  galvanometer  key,  as  the  figure  shows. 

Keeping  B  and  R^  alike,  and  of  fairly  high  value,  say  1,000 
ohms  each,  the  ratio  of  A  to  R^  may  be  varied,  so  that  the  gal- 
vanometer shows  no  deflection  whether  its  key  and  the  battery 
key  are  kept  closed  or  the  former  closed  and  the  latter  tapped. 

V  7? 
When  this  adjustment  is  reached,  S2  =  — ^—  . 


252      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


SECOHMETER   METHOD. 

The  secohmeter  is  a  mechanically  driven  commutator,  illus- 
trated in  Fig.  200,  which  is  provided  with  two  pairs  of  brushes, 
one  of  which  makes  contact  with  the  terminals  of  a  galvanometer 
and  the  other  with  the  source  of  E.M.F.  under  measurement. 
When  the  commutator  is  set  in  rotation,  it  reverses  the  direction 
of  the  battery  current  through  the  circuit  and  simultaneously 
reverses  the  connections  of  the  galvanometer  to  the  circuit,  so 
that  the  effort  on  the  galvanometer  needle  is  always  exerted  in 
one  direction  and  a  steady  deflection  maintained  in  spite  of  the 
current  reversals  through  the  circuit  under  test.  With  the  aid 


FIG.  200. 

of  this  piece  of  apparatus,  an  unknown  inductance  can  be 
measured  in  terms  of  a  known  one  by  the  following  method 
(due  to  Maxwell).  In  Fig.  201,  S  is  the  standard  inductance, 
A^  the  unknown  inductance,  and  R  and  R}  two  adjustable  non- 
inductive  resistances.  When  the  secohmeter  handle  is  turned, 
the  battery  circuit  being  closed,  the  ratio  of  R  to  R^  may  be 
adjusted  until  the  galvanometer  shows  no  deflection.  If  the 
same  adjustment  is  such  that  there  is  no  galvanometer  deflec- 

V7? 

tion  when  the  secohmeter  commutator  is  at  rest,  S  =. l-  • 

R 


MEASUREMENT  OF  INDUCTANCE.  253 


INDUCTANCE  WITH   ADJUSTABLE   STANDARDS. 

If  the  variable  standard  self-inductance  described  and  illus- 
trated on  page  36  be  used  in  place  of  the  single  value  standard 
S  in  the  preceding  paragraph,  the  measurement  becomes  simpli- 
fied, since  after  adjusting  R  and  R^  so  that  there  is  no  galva- 
nometer deflection  with  a  steady  current  it  is  only  necessary  to 
set  the  secohmeter  in  operation  and  turn  the  button  on  the  adjust- 


Gal. 


FIG.  201. 

able  standard  until  the  galvanometer  is  again  at  zero,  whereupon 
the  unknown  inductance  may  be  calculated  from  the  formula 

Cf  T> 

=       already  given. 

INDUCTANCE   BY   CALCULATION. 

In  a  few  instances,  with  suitably  shaped  coils,  inductance  may 
be  obtained  with  a  fair  degree  of  accuracy  by  calculation.  The 
simplest  case  is  when  the  inductance  is  in  the  shape  of  a  con- 
ductor coiled  up  to  make  a  solenoid  whose  diameter  is  small  as 
compared  with  its  length.  With  such  a  coil  the  value  of  the 
inductance  is 

4  7T2  nz  r* 


254      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

in  which  n  is  the  number  of  turns  of  wire,  r  is  the  mean  radius 
of  the  turns  in  centimeters,  and  I  the  over-all  length  in  centimeters. 
This  formula  is  theoretically  applicable  only  to  solenoids  of 
infinite  length,  but  the  error  introduced  when  applying  it  to 
solenoids  having  a  length  of  at  least  ten  times  their  diameter  is 
negligible  for  many  practical  purposes. 


MUTUAL  INDUCTANCE. 
NICHOLS  METHOD. 

The  quantity  of  electricity  that  is  momentarily  discharged 
through  a  circuit  connecting  the  terminals  of  a  coil  inductively 
influenced  by  a  neighboring  current  carrying  coil,  varies  in 
direct  proportion  to  the  strength  of  the  current  through  the 
influencing  coil  and  inversely  as  the  resistance  in  its  own  circuit. 


FIG.  202. 

It  is  also  dependent  upon  the  mutual  inductance  between  the 

coils ;  in  other  words,  the  relationship  is  Q  =  ——-  where  Q  is 

H 

the  quantity  of  electricity  momentarily  flowing  through  the 
influenced  coil,  R  the  resistance  of  that  coil,  I  the  current  that 
has  been  caused  to  flow  through  the  other  coil,  and  M  the  co- 
efficient of  mutual  inductance. 

To  measure  mutual  inductance  utilizing  this  formula,  con- 
nections are  made  as  in  Fig.  202.  Here  P  is  the  coil  through 
which  battery  current  is  passed,  and  8  the  one  in  which  current 
is  induced  when  the  strength  of  that  in  the  former  is  varied. 

The  value  of  Q  in  the  formula  must  be  determined  from  the 
characteristics  of  the  galvanometer  employed.  These  character- 
istics are  preferably  found  by  charging  a  condenser  of  known 
capacity  with  a  standard  cell  and  then  discharging  this  through 
the  instrument,  as  before  described.  /  is  measured  by  an 
ordinary  direct  current  ammeter,  A,  inserted  in  the  primary 


MEASUREMENT  OF  INDUCTANCE. 


255 


circuit  as  shown,  and  the  value  of  the  current  is  adjusted  at  will 
with  the  aid  of  the  resistance  D.  R  in  the  formula  is  the  resist- 
ance of  the  whole  secondary  circuit,  including  the  galvanometer 
and  adjustable  resistance  r,  and  may  be  measured  by  any  of  the 
conventional  methods  already  described. 

The  ammeter,  A,  for  measuring  the   current  in  the  primary 
circuit  should  be  of  low  range ;  in  fact,  if  the  current  values 


OffffTOT 


JWSUL 


--dscMtkU- 


FlG.  203. 


employed  are  reckoned  in  milliamperes  the  results  will  be  in 
millihenrys,  which  is  the  unit  usually  employed. 


MAXWELL  S    METHOD. 

This  involves  the  use  of  a  standard  of  mutual  inductance,  and 
the  test  is  made  as  shown  in  Fig.  203,  in  which  72  and  Rl  are 
adjustable  resistances  and  M  the  standard  pair  of  coils.  The 
values  of  the  resistances  are  varied  until  the  galvanometer 
shows  no  deflection  when  the  battery  circuit  is  rapidly  made  and 
broken,  at  which  time  the  ratio  M :  Ml:  :  R :  R^  holds  good. 

In  making  this  test  great  care  must  be  taken  to  separate  the 
standard  and  unknown  inductances  by  a  distance  sufficient  to 
prevent  any  possibility  of  mutual  interference  by  their  own 
mutually  inductive  actions. 


CAREY-FOSTER    METHOD. 


If  a  pair  of  coils  whose  mutual  inductance  is  to  be  determined, 
a  pair  of  adjustable  resistances,  a  galvanometer,  an  adjustable 
condenser,  a  battery,  and  a  key  are  interconnected  as  shown  in 


256       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


Fig.  204,  we  have  another  method  of  measuring  mutual  induc- 
tance. The  ratio  of  R  to  R^  and  the  value  of  the  capacity,  (7, 
must  be  adjusted  until  there  is  no  galvanometer  deflection 
whether  the  battery  circuit  is  held  closed  or  whether  it  is  being 


FIG.  204. 


rapidly  made  and  broken.  When  this  condition  is  attained,  the 
mutual  induction  may  be  calculated  from  the  formula  M  =  C  Rr, 
where  r  is  the  resistance  of  R^  plus  that  of  e.  (See  Phil.  Mag. 
Vol.  XXIII,  p.  121.) 


CHAPTER   XL 

MISCELLANEOUS   DETERMINATIONS. 
WAVE  FORMS. 

THE  determination  of  the  curves  depicting  the  rate  of  variar 
tion  in  strength  and  direction  of  the  E.M.F.  and  current  from 
an  alternating  source  is  often  of  considerable  importance,  par- 
ticularly as  affecting  the  design  of  auxiliary  appliances.  Such 
curves  are  not  obtainable  from  apparatus  ordinarily  forming  part 
of  an  engineer's  equipment,  but  may  be  derived  in  the  following 
ways: 

Contact  Methods. 

One  method  of  obtaining  the  E.M.F.  curve  of  a  given  alter- 
nating current  dynamo  is  to  rigidly  attach  a  disk  of  insulating 
material,  as  diagrammatically  shown  in  Fig.  205,  to  the  armature 
shaft,  so  that  it  rotates  at  the  same  speed  and  maintains  a  fixed 

b 


FIG.  205. 

position  relative  to  the  armature  windings.  On  the  periphery 
of  this  disk  there  is  located  a  metal  block  connected  to  the 
windings,  and  a  brush  arranged  to  bear  on  the  disk  makes  con- 
tact with  the  block  once  in  every  revolution  of  the  armature. 
If  the  brush  is  held  fixed,  the  difference  of  potential  between  it 
and  the  other  terminal  of  the  armature  winding  is,  at  the  instant 
of  contact,  that  generated  by  the  coil  when  it  is  in  the  position 

257 


258       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


relative  to  the  pole  pieces  corresponding  to  the  brush  position. 
As  this  potential  is  applied  to  the  brush  several  times  per  sec- 
ond with  machines  of  the  usual  commercial  frequencies,  and 
always  in  the  same  direction,  its  value  may  be  read  off  from  the 
indications  of  an  ordinary  direct  current  voltmeter  connected 
between  the  brushes  a  and  &,  in  Fig.  205.  By  rotating  the 
contact  brush  to  different  angular  positions  around  the  armature 

shaft,  the  E.M.F. 
values  may  there- 
fore be  determined 
for  any  position  of 
the  armature  con- 
ductors and  the 
values  thus  obtained 
plotted  so  as  i^o  give 
the  curve  required. 
A  convenient  de- 
vice for  making  con- 
tact at  various  angu- 
lar positions  of  the 
armature  is  the  Fes- 
senden  portable  con- 
tact maker,  shown 
in  Fig.  206.  This 
consists  of  a  hard 
rubber  disk  provided 
with  a  pointed 
spindle  which  is 
pressed  against  the 
end  of  th  armature 
shaft  like  an  ordi- 
nary tachometer.  The  handle  shown  is  secured  to  the  frame 
carrying  the  brushes  and  terminals,  and  the  angle  at  which  con- 
tact is  being  made  is  read  off  from  the  position  of  the  scale 
relative  to  the  pointer-like  end  of  the  rod  carrying  the  heavy 
steadying  bob. 

In  order  that  the  indications  of  a  voltmeter  used  with  a  de- 
vice like  the  foregoing  may  be  rigorously  correct,  it  is  necessary 
that  the  same  be  of  a  type  which  does  not  draw  current 
from  the  circuit,  a  fact  which  at  once  suggests  the  use  of  a 


FIG.  206. 


MISCELLANEOUS  DETERMINATIONS. 


259 


potentiometer  method,  that  is  to  say,  balancing  the  unknown 
potential  against  an  opposing  known  one. 

To  do  this  with  a  regular  potentiometer,  a  contact  maker,  and 
the  necessary  accessories,  and  to  plot  the  observed  readings  on 
section  paper,  is,  however,  a  tedious  procedure ;  in  fact,  it  may 
require  some  hours  if  the  current  being  investigated  is  not  of  a 
smooth  wave  form.  The  following  instrument  was  devised  for 
the  purpose  of  minimizing  this  objection. 


Rosa   Curve   Tracer. 

The  plan  employed  in  the  Rosa  curve  tracer  is  shown  in  Fig. 
207,  the  apparatus  being  in  this  case  connected  up  to  record  a 
current  curve.  AB  is  a  non-inductive  resistance  of  known  value 


FlG.  207. 

connected  in  series  in  the  line  under  test,  CM  is  a  contact 
maker,  MN  is  a  resistance  wire  wound  on  and  supported  by  an 
insulating  cylinder,  P  is  a  contact  brush  sliding  over  NM,  and 
Q  is  a  permanent  connection  to  B,  the  galvanometer  Gr  being 
inserted  in  that  circuit.  Current  is  supplied  by  a  battery  B 
having  a  potential  that  is  indicated  by  the  voltmeter  Vm.  The 
frame  carrying  the  sliding  contact  P,  by  means  of  which  contact 
may  be  made  at  any  portion  of  the  wire  resistance  forming  the 
coil  MN,  carries  also  the  point  J7,  which  makes  the  record.  D 
is  a  drum  to  which  the  record  chart  is  secured. 


260       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

With  any  given  load  on  the  circuit  under  test,  the  contact  P 
may  be  placed  at  some  point  on  the  wire  MN  where  the  galva- 
nometer G-  will  show  no  deflection.  At  this  time  the  difference 
of  potential  between  P  and  Q  is  evidently  the  same  as  that  be- 
tween A  and  B,  and  is  therefore  the  instantaneous  value  of  the 
impressed  current  with  the  position  of  the  contact  brush  that  at 
the  time  of  making  the  reading.  If  the  brush  angle  is  now 
changed,  P  must  be  moved  in  order  to  bring  the  galvanometer 


FIG.  208. 


to  zero  once  more,  and  this  operation  must  be  repeated  for  each 
angular  position  of  the  brush.  For  that  portion  of  the  current 
curve  in  which  the  current  is  flowing  in  a  reversed  direction 
through  AB,  P  must  be  placed  on  the  other  side  of  Q  from  that 
shown  in  order  to  obtain  a  balance.  The  pointer  F  does  not 
bear  continuously  on  the  chart,  but  is  struck  against  it  by  means 
of  a  bar,  and  thus  makes  a  dot  for  each  reading.  When  the 
lever  that  operates  the  bar  is  being  returned  to  its  first  position, 
it  works  a  ratchet  that  rotates  the  paper  drum  the  proper  distance 
ahead,  and  at  the  same  time  closes  a  circuit  that  energizes  an 
electromagnet  forming  part  of  the  contact  maker,  which  in  that 


MISCELLANEOUS  DETERMINATIONS.  261 

way  has  its  contact  brush  advanced  a  corresponding  amount, 
leaving  everything  ready  for  the  next  reading.  The  operation 
is  therefore  reduced  to  the  simple  act  of  moving  the  contact 
along  until  the  galvanometer  shows  no  deflection,  raising  and 
lowering  a  lever,  and  repeating.  It  is  claimed  that  twenty 
points  a  minute  can  be  printed  by  an  experienced  op- 
erator. 

The  curve  tracer  is  shown  in  Fig.  208.     The  crank  at  the 
right  is  turned  to  cause  the  contact  P  to  travel  along  its  wire, 


FlG.  209. 

and  the  lever  at  the  left  is  the  one  used  for  printing,  etc. 
The  contact  maker  is  shown  in  Fig.  209. 

Instead  of  using  a  potentiometer  method,  the  instantaneous 
values  of  a  fluctuating  current  at  various  points  on  the  curve 
may  be  satisfactorily  determined  with  the  aid  of  a  contact  maker, 
a  condenser,  and  a  galvanometer. 

Referring  to  Fig.  210,  the  E.M.F.  at  the  instant  of  contact  is 
used  to  charge  the  condenser  C  of  known  capacity.  Subse- 
quently the  key  JVis  depressed,  and  the  deflection  of  the  gal- 
vanometer G-  noted.  The  throw  of  the  galvanometer  is  of 
course  proportional  to  the  condenser  charge,  and  the  latter  to 
the  charging  E.M.F.,  so  that  the  throws  are  proportional  to  the 
instantaneous  potentials  at  the  different  positions  of  the  contact 
brush. 

The  Blondel  contactor  shown  in  Fig.  211  simplifies  making 
this  test.  An  inspection  of  the  figure  will  show  that  if  the  disk 
D  rotates  in  synchronism  with  the  source  of  supply,  contact  is 
first  made  so  that  the  condenser  is  charged  by  the  E.M.F.  at 
the  point  of  rotation  of  the  armature  determined  by  the  setting 


262        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

of  the  brush,  and  that  the  condenser  is  immediately  afterward 
discharged  through  the  galvanometer.     The  impulses  thus  sent 


FIG.  210. 


follow  one  another  with  such  rapidity  that  the  galvanometer 
deflection  becomes  a  steady  one,  and  there  is  therefore  nothing 


FIG.  211. 


to  do  but  set  the  contact  maker  at  different  angles,  and  observe 
the  deflections  due  to  each  in  order  to  obtain  the  relative  values 
of  the  ordinates  at  different  points  on  the  curve. 


MISCELLANEOUS  DETERMINA  TIONS. 


263 


Duddell  Oscillograph. 

This  instrument,  illustrated  by  Fig.  212,  is  one  in  which  one 
or  more  strips  of  conducting  material  traversed  by  the  currents 
whose  wave  forms  are  to  be  determined  are  placed  in  an  ex- 
tremely powerful  magnetic  field.  The  latter  is  furnished  by 
a  circular  electromagnet 
having  its  poles  shaped 
so  as  to  give  a  very  nar- 
row and  intense  field, 
and  energized  by  several 
separate  sets  of  coils,  in 
order  that  by  intercon- 
necting them  in  different 
ways  the  necessary  ex- 
citing current  may  be 
obtained  from  circuits  of 
different  E.M.F.'s.  In 
the  apparatus  illustrated 
there  are  three  mirrors 
similar  to  those  used  in 
ordinary  galvanometers, 
but  smaller  and  lighter. 
One  is  stationary  and 
furnishes  a  reference  line. 
Each  of  the  other  two  is 
attached  to  a  pair  of 
metal  strips  electrically 
connected  at  their  lower 
extremities,  and  held  in 
tension  by  the  adjust- 
able spring  arrangement 
shown  projecting  above  the  rest  of  the  instrument.  The  path 
of  the  current  is  up  one  and  down  the  other  strip  of  a  pair  in 
each  case.  Owing  to  the  tension  of  the  strips  the  time  required 
for  a  complete  oscillation  of  a  mirror  is  exceedingly  small, 
namely,  about  .0001  second.  When  current  is  sent  through 
either  of  the  pair  of  strips,  the  reaction  between  that  current 
and  the  field  causes  the  attached  mirror  to  deflect  an  amount 


264        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

proportional  to  the  current  strength,  and  because  the  period  of 
vibration  is  so  small,  the  mirror  position  may  continuously  vary 
with  a  changing  current  strength,  and  follow  it  exactly.  If  the 
beam  of  light  from  the  mirror  were  simply  projected  on  a  trans- 
lucent scale  plate,  the  visible  result  would  be  merely  a  straight 
luminous  band  on  the  plate.  When,  however,  the  light  beam  is 
first  thrown  on  a  mirror  that  is  oscillated  by  a  cam  synchron- 
ously driven,  and  whose  axis  is  at  right  angles  to  that  of  the 
oscillograph,  the  ray  traces  on  the  surface  to  which  it  is  re- 
flected, a  curve  which  is,  of  course,  the  current  curve.  Owing 
to  the  rapidity  with  which  the  successive  values  in  each  curve 
are  repeated  and  follow  one  another,  persistence  of  vision 
causes  the  observer  to  see  on  the  screen  a  curve  which  is  the 
current  curve.  As  the  fixed  mirror  shows  a  straight  line  under 
the  same  conditions,  we  have  all  the  information  that  is  necessary 
in  order  to  be  able  to  observe  the  character  of  any  current. 
Where  records  of  this  are  to  be  kept,  it  is  a  simple  matter  to 
substitute  a  photographic  plate  for  the  screen. 

The  object  in  having  two  sets  of  strips  each  with  its  attached 
mirror  is  to  enable  one  instrument  to  show  on  a  scale  or  record 
on  photographic  paper,  simultaneously,  the  varying  values  of 
both  the  potential  and  current  curves  of  any  circuit.  This  form 
is  called  the  "  Double  Oscillograph." 


HotMiss  Oscillograph. 

In  this  instrument  the  stationary  magnetic  field  is  furnished 
by  a  powerful  laminated  permanent  magnet,  and  instead  of 
having  movable  strips  through  which  the  current  flows,  station- 
ary coils  are  provided  inside  of  which  again  there  are  located 
minute  soft  iron  needles  suspended  by  quartz  fibers.  It  is  plain 
that  this  instrument  is  merely  a  special  form  of  Thompson  gal- 
vanometer, just  as  the  Duddell  oscillograph  is  merely  a  special 
form  of  d'Arsonval  galvanometer. 

The  dimensions  of  the  movable  iron  needles  in  the  Hotchkiss 
device  are  so  small  that  the  period  of  oscillation  of  the  systems 
formed  of  these  and  their  respective  mirrors  is  about  the  same 
as  the  moving  system  of  the  Duddell  device,  that  is,  .0001 
second. 


MISCELLANEOUS  DETERMINATIONS. 


265 


One  of  the  double  oscillographs  of  this  pattern  is  shown  in 
plan  and  elevation  by  Fig.  213,  the  two  moving  systems  being, 
as  shown,  in  two  independent  magnetic  fields  instead  of  one 
common  one.  The  rectilinear  deflections  of  the  mirrors  are 
translated  into  curves  showing  the  current  strength  variations, 
by  using  a  synchronous  motor  driven  mirror,  as  in  the  Duddell 
oscillograph. 

FREQUENCY  METERS. 

Hartmann  and  Braun  Frequency  Meters. 

If    an  electromagnet  be  excited    by  an  alternating  current, 
and  a  tuning  fork  is  presented  to  one  pole  of  this  magnet,  the 


FIG.  213= 

successive  attractions  will  set  the  tuning  fork  in  vibration  if  the 
period  of  the  fork  is  the  same  as  that  of  the  alternations,  but 
the  fork  will  not  respond  if  this  sympathy  does  not  exist.  The 
Hartmann  and  Braun  frequency  meter  takes  advantage  of  this 
fact.  Referring  to  Fig.  214,  showing  a  switchboard  pattern  of 
such  a  device,  the  twelve  white  rectangular  patches  appearirg  in 
the  two  openings  cut  in  the  dial  plate  are  the  ends  of  steel  strips 
or  reeds  bent  over  at  right  angles  to  the  length  of  the  strips 
proper  and  painted  white  to  make  them  more  conspicuous. 
Opposite  each  reed  there  will  be  noticed  a  numeral,  100.5,  101, 


266       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

101.5,  etc.,  these  being  their  respective  vibration  rates  in  alter- 
nations per  second.  Between  the  two  rows  of  reeds  is  a  lami- 
nated core  electromagnet  (not  visible  in  the  illustration)  through 
whose  windings  is  passed  the  alternating  current  whose  fre- 
quency is  to  be  measured.  Evidently  now  if,  as  shown  by  the 
cut,  the  end  of  reed  98.5  vibrates  over  its  full  amplitude,  the 
ninety-eight  and  ninety-nine  reeds  at  the  same  time  vibrating 
slightly,  the  current  impulses  follow  one  another  at  intervals 
corresponding  to  the  vibration  period  of  reed  98.5,  that  is  to  say 
its  frequency  is  98.5  alternations  per  second. 

Instead  of  visually  noting  which  of  a  series  of  reeds  of  differ- 
ent periods  is  vibrating  over  a  maximum  amplitude,  the  accous- 


FIG.  214. 


tic  properties  of  such  strips  may  be  utilized,  provided  that  their 
rate  is  one  giving  a  note  that  is  audible  to  the  human  ear, 
namely  between  fifty  and  one  hundred  and  fifty  vibrations  per 
second. 

A  Hartmann  and  Brauii  instrument  of  this  kind,  with  its  outer 
casing  removed  to  show  the  arrangement  of  the  mechanism,  is 
illustrated  in  Fig.  215.  The  various  reeds,  in  this  case  of  peri- 
ods from  79  to  110  inclusive,  are  arranged  on  a  circular  frame- 
work which  may  be  rotated  by  means  of  the  central  handle  so 
as  to  successively  present  them  to  the  magnet  system. 

This  system  is  composed  of  two  magnets  which  when  brought 


MISCELLANEOUS  DETERMINATIONS.  267 

together  by  means  of  the  handles  shown  act  as  one.  The 
double  magnet  arrangement  is  convenient  in  that,  after  the  fre- 
quency of  the  circuit  under  test  has  been  determined  by  rotating 
the  central  button  until  a  note  of  maximum  volume  is  heard, 
the  magnets  may  be  separated  and  the  otherwise  continuous 
sound  which  might  De  annoying,  stopped. 

They  still  perform  a  useful  service,  however,  as  if  the  fre- 
quency of  the  circuit  should  either  increase  or  decrease,  one  or 
the  other  of  the  magnets  would  set  its  corresponding  reed  in 
vibration  and  the  note  then  heard  serves  as  a  warning  of  the 
change. 

In  both  the  visual  and  acoustic  types  of  meters  the  range  of 


FIG.  215. 

measurement  may  be  doubled,  or  rather  each  reed  may  be  made 
to  respond  to  a  frequency  double  that  of  its  normal  one  by  add- 
ing either  a  few  turns  of  direct  current  exciting  winding  or  by 
inserting  a  permanent  magnet  to  polarize  the  reeds. 

This  follows,  as  a  non-polarized  strip  is  evidently  attracted  by 
each  current  impulse  irrespective  of  direction  of  the  alternating 
current  flow,  whereas  if  a  strip  be  polarized  magnetically  the 
current  flow  in  one  direction  attracts  and  that  in  the  reverse 
direction  repels  it,  and  there  is  hence  required  double  the  original 
frequency  to  give  the  same  number  of  attractive  efforts. 


268       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

The  accuracy  of  these  instruments  is  extremely  good,  and 
their  simplicity  and  the  absence  of  what  in  the  accepted  sense 
of  the  term  are  moving  parts  commends  them  for  general  ser- 
vice. 

/Schmidt  Frequency  Meter. 

Another  acoustic  device  for  measuring  the  frequency  of 
alternating  currents  is  that  due  to  K.  E.  F.  Schmidt. 

In  it  the  current  under  investigation  is  passed  through  a 
telephone  receiver  and  the  diaphragm  of  that  receiver  placed 
before  the  open  end  of  a  tube  about  one  inch  distant  there- 
from. The  tube  is  about  one  inch  in  diameter  and  two  or 
three  feet  long,  and  has  within  it  a  piston  which  may  be  moved 
backward  and  forward  by  means  of  a  handle  so  as  to  vary  the 
effective  tube  length.  The  vibrations  of  the  receiver  diaphragm 
tend  to  set  the  air  imprisoned  in  the  tube  into  vibration  also, 
and  if  the  piston  is  moved  in  and  out,  a  position  can  be  found 
where  the  tone  emitted  by  the  tube  is  of  a  maximum  volume.  The 
vibration  periods  of  the  diaphragm  and  the  air  column  are  then 
alike,  and  hence  the  frequency  may  be  read  off  directly  from  a 
scale  properly  marked  on  the  piston  rod. 

Manzetti  Frequency  Meter. 

In  this  instrument  there  is  a  moving  system  which  consists  of 
a  copper  disk  mounted  rigidly  on  the  same  axis  with  a  parallel- 
epiped of  laminated  iron.  This  element  is  either  pivoted  or 
carried  by  a  quartz  fiber,  and  the  copper  and  iron  used  therein 
are  acted  upon  by  separate  sets  of  coils.  The  two  sets  of  coils 
are  connected  across  the  circuit  with  a  resistance  in  series  with 
each  pair.  When  current  flows,  the  turning  effort  exerted  on 
the  iron  is  independent  of  the  frequency,  while  in  the  copper 
disk  it  is  a  function  of  the  frequency.  If,  therefore,  the  two 
sets  of  coils  are  adjusted  so  that  at  the  standard  frequency  the 
torques  exerted  by  them  are  equal  and  opposite,  there  will,  of 
course,  be  no  deflection,  but  if  the  frequency  changes,  a  deflec- 
tion will  be  produced  because  of  the  different  torque  then 
exerted  by  the  copper  disk.  This  torque  can  be  measured 
either  on  the  dynamometer  principle  mentioned  on  page  165,  or 
may  be  used  to  urge  a  needle  over  an  appropriate  scale  against 
a  constantly  increasing  spring  pressure.  In  the  latter  event  the 
scale  may  be  calibrated  so  as  to  indicate  frequencies  directly. 


MISCELLANEOUS  DETERMINATIONS. 


269 


WestingJiouse  Frequency  Indicator. 

This  instrument  is  illustrated  in  Fig.  216,  and  consists  of  two 
voltmeter  movements  so  connected  together  mechanically  that 
they  tend  to  move  the  pointer  in  opposite  directions.  In  series 
with  one  of  the  movements  there  is  a  non-inductive  resistance, 
and  in  series  with  the  other,  a  resistance  that  is  highly  inductive. 
If  the  frequency  changes,  the  torque  exerted  by  the  two  wind- 
ings will  therefore  become  unbalanced,  that  of  the  inductive 
winding  being  relatively  decreased,  and  if,  as  is  the  case,  the 
construction  of  the  apparatus  is  such  that  when  the  needle 
swings  in  either  direction,  the 
torque  of  the  member  tending  to 
swing  it  in  opposite  direction 
is  increased,  it  will  evidently 
move  until  the  two  forces  are 
again  balanced.  The  scale  is 
empirically  graduated  by  passing 
currents  of  known  frequency 
through  the  device  and  marking 
on  the  scale  the  different  posi- 
tions assumed  by  the  needle. 
The  indications  of  these  instru- 
ments are  influenced  by  wave 
form  as  well  as  frequency,  and 
they  are  hence  correct  only  on  the  wave  form  for  which  they 
are  adjusted. 

PHASE   INDICATORS. 

Two  alternating  currents  of  like  frequency  are  said  to  differ 
in  phase  when  they  do  not  simultaneously  attain  their  respec- 
tive maximum  positive,  maximum  negative,  and  zero  values. 
The  difference  in  phase  is  usually  expressed  in  terms  of  the 
cosine  of  the  angle  </>  between  the  two  radii  passing  through 
the  corresponding  zero  values,  when  the  circumference  of  a 
circle  whose  perimeter  is  one  wave  length  is  used  as  the  refer- 
ence line.  This  expression  for  phase  difference  is  rigorously 
correct  only  when  the  currents  are  sinusoidal,  and  not,  as  is 
frequently  the  case  in  practice,  when  they  are  of  different  wave 
forms. 


FIG.  216. 


270      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

Assuming  sine  waves,  we  would  have  in  an  alternating 
current  circuit  in  which  there  is  a  difference  in  phase  between 
the  potential  and  current  curves,  the  expression  P  =  E I  cos  <£ 
in  which  E  and  /  are  the  effective  potential  and  current  as 
measured  by  a  voltmeter  and  ammeter  of  the  static,  hot  wire,  or 
electromagnetic  type  before- described,  and  P  is  the  power. 

Phase  meters  are  instruments  for  indicating  the  value  of  the 
angle  <£. 

Voltmeter,  Ammeter,  and  Wattmeter  Method. 

If  the  difference  in*  phase  between  the  current  and  potential 
curves  in  an  alternating  current  circuit  is  desired,  one  way  to 
determine  it  is  to  use  a  wattmeter,  and  in  addition  to  insert  a 
voltmeter  and  an  ammeter  in  the  line.  If  all  three  readings  are 
observed  simultaneously,  the  cosine  of  the  angle  of  lag  may  be 
calculated  from  the  formula  P  =  E  I  cos  $  mentioned  above, 
all  of  the  factors  with  the  exception  of  cos  </>  being  known 
from  the  observation. 

Oscillograph  Method. 

The  double  oscillographs  described  on  page  264  may  be  used 
to  determine  the  difference  in  phase  between  two  alternating 
currents,  by  passing  one  through  one  of  the  movable  elements 
of  this  apparatus  and  the  other  through  the  other.  If  the 
resultant  figures  are  thrown  on  a  translucent  plate  or  are  photo- 
graphed, two  curves  will  appear  together  with  the  zero  or 
reference  line  made  by  the  fixed  mirror,  and  the  difference  in 
phase  can  be  scaled  off  therefrom.  Oscillographs  are  but  seldom 
available,  however,  so  that  this  method  is  in  very  restricted 
use. 

Dobrowolsky  Phase  Indicator. 

This  is  an  instrument  in  which  a  pointer  sweeping  over 
a  graduated  scale  shows  directly  the  difference  in  phase  between 
two  currents.  Referring  to  Fig.  217,  the  movable  element  to 
which  the  pointer  is  attached  is  a  disk  of  soft  iron  pivoted  at  its 
center  and  having  its  motion  opposed  by  a  volute  spring.  If 
the  current  through  the  two  sets  of  windings  shown  as  sur- 
rounding the  disk  at  right  angles  to  one  another  are  in  phase, 
no  force  will  be  exerted  to  rotate  the  disk.  If,  however,  a 


MISCELLANEOUS  DETERMINATIONS. 


271 


FIG.  217. 


phase  difference  exists,  there  is  set  up  a  rotary  magnetic  field, 

which  in  turn  exerts  a  torque  on  the  disk  and  tends  to  turn  it. 

If  the  changes  in  strength  of  one  current  lag  behind  those  of 

the  other,  the  torque  will  be  in 

one  direction,  and  if  vice  versa 

the    needle   will    be    oppositely 

rotated.     The  instrument,  after 

being    calibrated    with    known 

phase  differences,  will  therefore 

indicate  not  only  the  difference 

in  phase,  but  which  current  is 

leading  and  which  is  lagging. 

If  the  instrument  is  being 
used  on  a  circuit  in  which  both 
the  frequency  and  the  effective 
potential  are  constant,  the  scale 
graduation  may  be  made  to  show 
either  the  effective  amperage  or 

the  wattless  current  —  that  is,  the  component  of  the  total  cur- 
rent that  is  not  effective  in  doing  work  —  flowing  through  it. 
An  instrument  so  graduated  is  frequently  convenient  for  use  in 
central  stations. 

Hartmann  and  Braun  Phase  Indicator. 

This  instrument  is  somewhat  similar  to  an  indicating  watt- 
meter, having  a  stationary  coil  through  which  the  whole  current 
to  be  measured  is  passed.  The  movable  element,  however, 
instead  of  consisting  of  but  one  fine  wire  coil,  consists  of  two 
such  mounted  with  their  planes  at  right  angles,  and  supported 
above  and  below  by  pivots. 

Current  is  led  into  and  out  of  these  windings  through  flexible 
silver  strips  so  fine  that  no  appreciable  force  prevents  the  needle 
attached  to  the  coil  pair  from  assuming  any  position  within  the 
limit  of  its  travel.  One  of  the  instruments  is  shown  in  Fig. 
218.  In  series  with  one  of  the  two  movable  coils  there  is  placed 
a  non-inductive  resistance,  and  the  other  coil  has  in  series  with 
it  a  highly  inductive  resistance,  as  is  indicated  by  the  two  spools 
mounted  on  the  transformer-like  core.  The  non-inductive  resis- 
tance and  its  spool  are  connected  in  parallel  with  the  inductive 
resistance  and  its  spool,  a  non-inductive  resistance  being  placed 


272       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

in  series  with  the  pair  to  cut  down  the  applied  potential.  Owing 
to  the  presence  of  an  inductance  in  one  coil  circuit  and  the  fact 
that  there  is  none  in  the  other,  the  currents  in  the  two  differ  in 
phase  by  ninety  degrees.  These  displaced  currents  set  up  a 
rotary  field,  which  in  turn  is  located  within  the  influence  of 
the  field  due  to  the  current  through  the  stationary  winding. 
When,  therefore,  the  current  through  the  series  coil  differs 
in  phase  from  that  flowing  through  the  potential  coils  by  a 
given  .amount,  the  potential  coils  will  assume  one  fixed  position 
where  the  rotative  effort  is  zero.  When  the  phase  difference 
between  two  currents  changes,  however,  the  angle  of  the  double 


FIG.  218. 

coil  movable  element  relative  to  the  fixed  one  must  change  also. 
The  scale  over  which  the  needle  of  this  instrument  swings  may 
therefore  be  graduated  empirically  to  indicate  phase  difference. 
It  should  be  noted  that  while  this  form  of  device  is  inde- 
pendent of  the  amount  of  current  flowing  and  of  the  E.M.F. 
applied,  it  is  dependent  on  the  frequency  and  must  be  specially 
calibrated  for  each  frequency,  if  correct  results  are  to»  be  had. 

SYNCHRONISM    INDICATORS. 

In  order  that  two  sources  of  alternating  current  may  be  con- 
nected in  parallel  so  as  to  jointly  supply  current  to  any  given 


MISCELLANEO US  DETERMINA  TIONS. 


273 


circuit,  it  is  not  only  desirable  but  in.  many  instances  absolutely 
necessary,  that  some  device  be  employed  which  will  indicate 
when  the  current  furnished  by  the  source  about  to  be  added  is 
in  synchronism  with  the  one  already  delivering  current,  in  order 
that  it  may  be  connected  at  that  time.  If  it  were  coupled  in 
when  the  currents  are  out  of  phase,  an  interchange  of  current 
between  the  sources  would  ensue,  which  current  may  be  so  large 
as  to  cause  disastrous  results. 

Lamp  Synchronizers. 

The  simplest  form  of  apparatus  for  indicating  synchronism 
between  two  sources  of  alternating  current  is  shown  in  Fig. 
219.  Here  6r  and  Grr  are  the  sources,  T  and  Tf  transformers 
energized  by  them,  and  L  and  Lf  incandescent  lamps.  It  will 


FIG.  219. 

be  seen  that  the  secondary  windings  of  the  transformers  are 
connected  in  series.  If,  now,  the  currents  from  6r  and  6r'  are 
in  phase,  the  current  impulses  of  the  transformer  secondaries 
evidently  increase  in  value  simultaneously,  and  if  they  are  oppo- 
site in  direction,  no  current  will  flow  through  the  lamps  and 
these  will  remain  dark.  Should  there  be  a  difference  of  phase, 
some  current  will  flow  in  the  lamp  circuit,  and  this  will  be  a 
maximum  when  the  phases  are  180  degrees  apart;  that  is  to 
say,  when  the  currents  of  the  two  secondaries  are  assisting  each 
other.  Hence,  if  6r  is  a  machine  already  running  and  G*  is  one 
to  be  thrown  in,  the  lamps  will  be  illuminated  and  extinguished 
in  rapid  succession  when  Grf  is  first  started,  and  these  successive 
periods  of  light  and  darkness  will  succeed  each  other  with 
decreasing  frequency  as  the  speed  of  rotation  of  &  rises  until  its 


274      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

speed  is  exactly  that  of  6r  and  the  current  delivered  thereby  in 
phase  therewith,  at  which  time  the  lamps  will  remain  dark. 
The  operation  of  connections  in  parallel  may  then  be  accom- 
plished by  closing  an  appropriate  switch.  By  reversing  the 
connections  of  the  secondary  of  either  one  of  the  two  trans- 
formers, the  lamps  will  be  burning  at  full  brilliancy  when  syn- 
chronism is  attained,  instead  of  being  extinguished'  at  that 
time. 

The  first  method  is,  however,  preferable,  as  after  watching 
lamps  during  the  time  at  which  6r''s  speed  is  being  raised  to  its 
desired  value  the  eye  becomes  fatigued,  and  it  is  more  difficult 
to  determine  the  instant  of  maximum  brilliancy  than  that  of 
complete  darkness. 

Voltmeter  Method. 

If  in  the  above  plan  an  alternating  current  voltmeter  is  sub- 
stituted for  the  two  lamps  its  indications  can  be  used  to  show 
the  attainment  of  synchronism  with  greater  accuracy  than  is 
possible  with  the  lamps.  As  alternating-current  voltmeters  are 
of  less  sensibility  near  zero  than  in  the  working  range  of  the 
scale,  or  in  other  words,  as  the  deflection  per  unit  of  potential 
difference  is  less  near  zero  than  up  the  scale,  it  is  advisable  to 
use  the  second  scheme  of  connections  mentioned ;  that  is,  the 
one  in  which  the  transformer  secondaries  are  connected,  so  that 
their  E.M.F.'s  assist  each  other  when  synchronism  is  attained. 
In  using  a  voltmeter  its  indications  are  merely  observed  until 
the  needle  is  practically  at  rest  at  a  maximum  indication, 
whereupon  the  incoming  machine  is  coupled  in  as  before. 

The  Mutter  Synchronism  Indicator. 

For  commercial  purposes  it  is  desirable  that  the  synchronizing 
apparatus  shall  show  not  only  when  synchronism  between  the 
incoming  generator  and  the  one  or  ones  already  supplying  cur- 
rent is  reached,  but  that  it  should  show  whether  the  incoming 
machine  has  too  high  or  too  low  a  frequency,  that  is,  whether  it 
is  running  too  fast  or  too  slow,  as  this  enables  the  attendant  to 
regulate  the  speed  accordingly. 

An  instrument  fulfilling  these  requirements  is  shown  in  Fig. 
220.  As  illustrated,  it  is  arranged  for  use  on  a  three-phase  cir- 
cuit. An  outer  ring  of  laminated  iron  is  wound  about  with  wire 


MISCELLANEOUS  DETERMINATIONS. 


275 


and  has  leads  tapped  into  its  convolutions  at  three  equidistant 
points.  These  three  terminals  are  attached  to  the  bus-bars. 
Within  this  ring  there  is  a  similar  one  provided  with  a  shaft  on 
which  it  rotates  and  having  three  collector  rings  so  that  electri- 
cal contact  may  be  made  through  brushes  to  three  leads  tapped 
into  its  winding  at  equidistant  points,  as  in  the  case  of  the 
stationary  ring.  The  brush  terminals  are  connected  to  those  of 
the  incoming  machine.  The  rotating  element  carries  a  target 
or  pointer,  so  that  its  movement  may  readily  be  discerned.  The 
electrical  connections  are  made  such  that  the  rotary  magnetic 
fields  set  up  by  each  of  the  rings  rotate  in  the  same  direction. 
When,  therefore,  the  frequency  of  the  potentials  supplied  to  the 


FIG.  220. 

two  windings  is  the  same,  the  fields  rotate  in  the  same  direction 
with  the  same  velocity  and  no  turning  effort  is  exerted  on  the 
inner  member.  When  the  two  are  not  in  phase,  however,  turn- 
ing effort  exists,  and  this  will  rotate  the  target  in  one  direction 
if  the  frequency  in  the  inner  ring  is  greater  than  that  in  the 
outer,  and  vice  versa  if  it  is  less.  A  stationary  target  secured 
to  the  outer  ring  is  used  as  a  reference  mark,  the  two  currents 
being  of  the  same  frequency  and  also  in  phase  when  the  r^  tating 
disk  masks  it.  It  should  be  noted  that  the  movable  disk  will 
always  remain  stationary  when  the  frequencies  are  the  same, 
but  that  its  vertical  position  is  assumed  only  when  the  currents 
are  also  in  phase.  At  other  times  the  angle  between  the  fixed 


276         ELECTRIC  AND  MAGNETIC   MEASUREMENTS. 

and  rotary  targets  is  a  measure  of  the  phase  angle  between  the 
currents. 

Lincoln  Synchronizer. 

In  this  instrument,  illustrated  in  Fig.  221,  the  position  of  a 
pointer  relative  to  a  fixed  mark  on  the  dial  over  which  it  rotates 
shows  the  phase  relations  and  difference  in  frequency  between 
two  alternating  currents  just  as  does  the  Muller  instrument  just 
described.  The  principle  of  operation  is,  however,  somewhat 
different. 

Referring  to  Fig.  222,  if  within  the  fixed  coil  F  there  is 
mounted  on  the  freely  movable  shaft  C  a  coil  A,  and  an  alter- 


FlG.  221. 

nating  current  is  passed  through  A  and  .Fin  series,  A  will  rotate 
until  it  takes  up  the  position  shown  parallel  to  the  plane  of  F. 
If  the  connections  between  A  and  F  are  reversed,  or,  which 
amounts  to  the  same  thing,  the  two  are  fed  by  currents  of  like 
frequencies  differing  in  phase  by  180  degrees,  A  will  rotate  180 
degrees.  The  force  tending  to  carry  the  coil  A  into  position  is, 
under  the  conditions  laid  down,  a  maximum  when  A  and  F  are 
parallel  and  it  is  zero  when  they  are  at  right  angles. 

An  instrument  with  a  single  coil  would  thus  have  a  "  dead 
center  "  position,  which  would  not  be  admissible. 


MISCELLANEOUS   DETERMINATIONS. 


277 


If,  however,  a  second  coil  B  be  added,  rigidly  secured  at 
right  angles  to  the  coil  A  and,  by  suitable  means,  the  current  in 
B  is  made  to  differ  in  phase  from  that  in  A  by  the  same  angle 
of  90  degrees,  B  will  be  in  a  position  where  it  exerts  a  maximum 
torque  when  A  is  at  its  zero  torque  position.  Hence,  if  there 
existed  a  difference  in  phase  of  90  degrees  between  the  currents  in 
A  and  F,  A  would  always  come  to  rest  at  right  angles  to  F,  and 
if  the  currents  in  the  two  were  in  phase,  A  would  turn  until  it 
was  parallel  to  F.  For  intermediate  phase  differences,  A  would 
assume  intermediate  angles,  and  hence  a  pointer  attached  to  A 
would  show  these  differences  on  a  dial. 

In  the  actual  instrument  the  coil  F  and  the  coils  A  and  B 
are  wound  on  laminated  iron  cores,  forming  a  structure  like  a 
small  motor.  The  difference  of  90  degrees  in  phase  between  the 
currents  in  A  and  B  is 
produced  by  putting  a 
highly  inductive  resist- 
ance in  series  with  one 
and  a  non-inductive  re- 
sistance in  series  with  the 
other.  The  currents 
whose  phase  and  fre- 
quency relati  ons  are 
sought  are,  of  course,  led,  the  one  through  the  windings  of 
F  and  the  other  through  the  coils  A  and  B  with  their  respective 
resistances. 

As  in  the  case  of  the  Miiller  instrument,  the  Lincoln  synchro- 
nizer exerts  a  considerable  torque,  so  that  it  is  possible  to  use  a 
robust  construction  with  heavy  bearings  without  introducing 
frictional  errors. 

SPEED    INDICATORS. 

Using  a  Magneto  and  a  Voltmeter. 

From  the  law  of  dynamo-electric  machines  the  potential  de- 
livered by  a  given  armature  rotating  in  a  magnetic  field  of  con- 
stant strength  is  directly  proportional  to  the  speed  of  rotation' 
of  the  armature.  In  other  words,  if  we  take  a  small  dynamo 
whose  field  is  supplied  by  permanent  magnets,  the  voltage  at  its 
brushes  varies  directly  with  the  speed  and  can  be  used  as  a 
measure  of  that  speed.  Fig.  223  shows  such  a  magneto  adapted 


278       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

to  be  belt  driven  by 'the  shaft  whose  speed  is  to  be  measured. 
The  revolution  indicator  used  with  it  is  simply  a  voltmeter, 
usually  of  one  of  the  commercial  types  described  on  page  193 
et  seq,  whose  scale  has  been  arbitrarily  calibrated  to  show  revo- 
lutions, by  noting  the  position  of  the  needle  when  the  magneto 
is  driven  at  various  known  speeds. 

This  method  of  speed  indication  has  the  advantage  that  the 
indicating  element  may  be  placed  at  any  reasonable  distance 
from  the  shaft  whose  speed  is  being  observed,  and  that*  the  rate 
of  rotation  is  .shown  at  each  instant  on  a  scale  which  may  be.-  of 
considerable  length  so  that  close  readings  can  be  had.  It  is 
also  possible  to  have  two  or  more  indicating  stations  with  the 


FIG.  223. 

one  magneto,  as  this  involves  only  the  addition  of  another  volt- 
meter. Direction  of  rotation  can  be  shown  also  by  using  a  per- 
manent magnet  type  voltmeter  having  the  zero  in  the  center  of 
the  scale,  in  which  event  the  needle  will  deflect  in  one  direction 
for  a  given  direction  of  rotation  of  the  magneto,  and  in  the  other 
for  the  other. 

Eddy  Current  Revolution  Indicator. 

In  Fig.  224  d  is  a  copper  cylinder  mounted  on  a  shaft  run- 
ning through  its  axis  and  driven  by  a  belt  from  the  shaft  whose 
speed  is  to  be  measured.  Pivoted  co-axially  within  the  cylinder 


MISCELLANEO  US  DE  TERM  IN  A  TIONS. 


279 


is  a  soft  iron  needle,  n,  s,  carrying  an  index  I,  that  sweeps  over 
a  graduated  scale.  The  cylinder  is  embraced  by  the  polar  ex- 
tremities of  a  permanent  magnet  $,  N.  When  the  cylinder  d 
is  set  in  rotation,  eddy  currents  are  generated  therein  as  it  cuts 
the  lines  of  force  of  the  permanent  magnet,  and  these  currents 
react  on  the  soft  iron  needle  and  tend  to  carry  it  along.  The 
tendency  of  n,  *,  to  rotate  is  opposed  by  the  directive  force  ex- 
erted on  it  by  the  permanent  magnet,  the  latter  acting  in  this 
respect  like  the  magnet  in  the  Ayrton  and  Perry  instrument 
mentioned  on  page  152.  The  scale  is  graduated  empirically 
as  in  the  case  of  the  magneto  and  voltmeter  combination  above 
named. 

Changes  in  strength  of  the  field  supplied  by  the  permanent 


magnet  affect  the  accuracy  of  the  indications  but  slightly,  be- 
cause as  this  changes,  the  eddy  currents  in  d  changing  likewise, 
the  restraining  force  on  the  needle,  n,  s,  changes  also.  Experi- 
ments show  that  the  strength  of  the  permanent  magnet;  may 
decrease  as  much  as  twenty  per  cent  without  causing  an  error 
in  indications  greater  than  one  per  cent. 

Several  modifications  of    this    form  of  speed  indicator  have 
been  proposed. 


280      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

Scholkmann  Speed  Indicator. 

In  this  device  a  small  inductor  alternator  is  driven  by  the 
shaft  whose  speed  of  rotation  is  to  be  measured.  The  moving 
part  is  a  simple  structure  of  laminated  iron  and  the  stationary 
portion  has  two  sets  of  windings  wound  on  alternate  poles. 
One  of  the  sets  is  energized  by  any  convenient  source  of  direct 
current,  such  as  a  storage  battery,  and  alternating  currents  are 
induced  in  the  other  by  the  rotating  core.  The  current  thus  set 
up  is  carried  through  wires  to  the  indicating  instrument,  which 
consists  of  a  small  two-phase  motor.  In  series  with  one  of  the 
windings  of  this  motor  there  is  placed  an  inductance  so  as  to 
cause  a  phase  displacement  and  give  rise  to  a  rotary  field  which 
in  turn  exerts  a  torque  on  the  armature,  the  latter  being  an 
aluminum  cylinder  which  is  rotated  against  the  tension  of  a  volute 
spring.  A  pointer  carried  by  the  cylinder  moves  over  *  a  prop- 
erly divided  scale  which  shows  the  speed  in  revolutions  directly. 
As  the  indications  of  the  indicator  are  dependent  on  the  fre- 
quency and  not  on  the  potential  of  the  current  supplied  to  it  by 
the  generator,  it  is  not  necessary  to  have  the  direct  current 
source  for  energizing  the  latter  of  constant  E.M.F. 

Stroboscopic  Methods. 

If  an  alternating  current  is  used  to  energize  a  source  of  light, 
such  as  an  arc  lamp  or  an  incandescent  lamp  with  a  thin  fila- 
ment, the  intensity  of  the  illumination  is  constantly  varying  as 
the  strength  of  the  current  varies.  This  phenomenon  is  not 
ordinarily  detected  by  the  eye,  because  on  commercial  circuits 
the  frequency  with  which  the  alternations  succeed  each  other  is 
greater  than  the  eye  can  detect,  whence,  because  of  the  persist- 
ence of  vision,  the  resulting  illumination  appears  uniform. 
These  successive  variations  in  illumination  may,  however,  be 
used  in  measuring  speed  of  rotation  if  the  number  of  alternations 
of  the  supply  circuit  is  known.  A  conspicuous  mark,  such  as 
a  streak  of  white  paint,  is  made  on  the  periphery  of  a  pulley  on 
the  shaft  whose  speed  is  to  be  taken,  and  this  mark  will  appear 
to  remain  stationary  when  illuminated  by  an  arc  lamp  fed  by 
the  current  named  if  the  number  of  alternations  and  revolutions 
are  alike,  as  the  illumination  from  the  arc  will  be  a  maximum  at 
the  same  angular  position  of  the  mark  at  each  revolution. 


MISCELLANEOUS  DETERMINATIONS.  281 

Should  the  apparatus  whose  speed  is  being  measured  be  driven 
from  a  source  that  is  not  rotating  in  synchronism  with  the  alter- 
nations, the  times  of  equal  illumination  will  occur  at  varying 
angular  positions  of  the  mark,  and  the  latter  will  therefore  seem 
to  the  eye  to  rotate  at  a  rate  that  increases  as  the  difference  in 
speed  between  the  two  sources  increases. 

The  source  of  illumination  in  stroboscopic  methods  of  meas- 
uring speeds  is  often  a  spark  from  the  secondary  winding  of 
an  induction  coil  whose  primary  is  excited  at  known  intervals, 
usually  through  a  contact  made  by  a  tuning-fork  whose  period 
has  been  determined. 


TRANSFORMER    TESTING. 

Efficiency. 

Transformers  waste  in  themselves  a  certain  amount  of  en- 
ergy, so  that  the  ratio  of  the  electrical  input  to  the  output  is  not 
unity.  The  losses  are  the  sum  of  the  following  factors  :  in 
the  primary  winding,  the  PR  loss,  this  being  the  energy  re- 
quired to  overcome  the  resistance  of  the  primary  winding ;  in 
the  secondary  winding,  a  corresponding  PR  loss ;  the  loss  due 
to  the  hysteresis  of  the  iron  forming  the  magnetic  circuit ;  and 
finally,  the  eddy  current  losses. 

The  PR  losses  in  both  primary  and  secondary  windings  are 
easy  of  measurement.  Direct  current  of  the  normal  full  ampere 
capacity  of  each  winding  may,  for  instance,  be  passed  and  the 
drop  across  the  winding  terminals  simultaneously  observed  by 
using  a  low-reading  voltmeter.  The  product  of  these  values  is, 
of  course,  PR  in  each  case.  Another  way  is  to  measure  the  re- 
sistance of  each  winding  by  any  of  the  suitable  methods  outlined 
in  the  chapter  on  resistance  measurements,  and  to  multiply  these 
values  by  the  squares  of  the  strengths  of  the  currents  which 
they  are  to  carry. 

The  sum  of  the  hysteresis  and  eddy  current  losses  can  be 
measured  indirectly  by  measuring  the  input  and  output  of  the 
transformer  by  indicating  wattmeters,  when  the  difference  be- 
tween the  indications,  less  the  sum  of  the  PR  losses  in  the 
primary  and  secondary  windings,  gives  the  result. 

Another  way  is  to  pass  full  normal  current  through  either  the 


282       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


primary  or  secondary  winding,  the  secondary  (or  primary  as  the 
case  may  be)  circuit  remaining  open  at  the  same  time,  and  in- 
serting a  wattmeter  in  the  energized  circuit.  The  wattmeter 
reading  gives  the  hysteresis  and  eddy  current  losses  plus  the 
primary  (or  secondary)  PR  loss.  The  latter  is  measured  sep- 
arately, as  already  explained,  and  then  deducted  from  the  result. 
To  have  this  test  an  accurate  one,  it  is  necessary  to  employ  a 
wattmeter  which  will  give  a  large  scale  deflection  on  a  very  low 
power  factor,  preferably  one  in  which  full  scale  is  given  with 
not  over  ten  per  cent  of  the  maximum  volt-ampere  capacity. 
The  instrument  must  also  give  accurate  readings  on  these  low- 
power  factors,  a  requirement  which  excludes  all  types  in  which 
the  angle  between  the  fixed  and  movable  coils  is  a  variable,  and 
practically  limits  the  choice  to  true  dynamometers  in  which  a 


Wattmeter 


Transformer* 


r 


torsion  head  must  be  rotated  manually  to  get  a  reading.  The 
connections  for  the  above  test  are  given  in  Fig.  227. 

The  method  of  testing  above  described  is  objectionable  for 
very  large  transformers,  as  it  calls  for  an  amount  of  current  suf- 
ficient to  fully  load  the  apparatus  during  the  time  that  the  test 
is  in  progress.  Where  it  is  not  possible  or  advisable  to  make 
this  heavy  draught  on  the  supply  lines,  Sumpner's  method  may 
be  brought  into  play. 

To  make  this  test,  two  identical  transformers  of  the  size  to 
be  tested  are  required,  and  there  is  needed  also  a  third  trans- 
former with  a  capacity  sufficient  to  supply  enough  current  to 
make  up  the  sum  of  the  losses  of  the  two  others,  but  whose 
efficiency  is  immaterial  and  need  not  be  measured.  Wattmeters 
and  an  ammeter  all  connected  in  circuit  as  shown  in  Fig.  228 
are  the  instruments  needed.  The  ammeter  A1  is  not  essential, 
and  the  same  is  the  case  with  the  voltmeter  V,  but  these  give 


MISCELLANEOUS  DETERMINATIONS. 


283 


data  of  interest.  From  the  connections  it  will  be  noted  that 
the  transformers  are  so  connected  that  each  supplies  the  other 
with  current,  the  small  transformer  receiving  enough  current 
from  the  mains  to  add  to  the  large  transformer  circuit,  current 
sufficient  to  overcome  the  losses  in  the  transformers  A  and  B. 
When  the  test  is  made,  the  regulating  resistance  R  is  varied 
until  the  ammeter  A  shows  that  full  current  is  flowing  through 
the  secondary  windings.  The  ammeter  and  voltmeter  in  the  pri- 
mary circuits  should  simultaneously  show  that  the  volume  and 
potential  of  the  current  flowing  in  these  is  the  normal  maximum. 
The  wattmeters  IF  and  W  will  then  give  the  desired  information, 
the  indications  of  W  giving  the  sum  of  the  iron  losses  in  the  two 
transformers,  and  W  the  copper  losses  of  the  two  plus  those  in 
the  leads  and  in  the  wattmeter  W  and  ammeter  A. 

Transformer  Insulation  Test. 

One  of  the  important  tests  to  which  every  transformer  should 
be  subjected  before  it  is  placed  in  circuit  is  that  to  determine 


Wattmeter 
W 


FlG.  228, 


the  insulation  resistance  of  its  windings.  To  have  the  results 
of  any  value,  it  is  necessary  that  they  be  made  with  high  ap- 
plied potentials,  as  it  is  found  that  the  behavior  of  the  insulating 
material  is  entirely  different  under  high  electrical  stresses  than 
under  low  ones.  The  best  test  is  the  rough  and  ready  one  of 
using  a  source  having  a  potential  at  least  double  that  of  the 
highest  voltage  to  which  the  device  will  be  connected  in  use, 
and  then  with  this  potential  testing  to  see  whether  a  breakdown 
can  be  made  through  the  primary  insulation  to  the  core,  through 
the  secondary  insulation  to  the  core,  or  from  the  primary  to  the 


284       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

secondary  winding.  In  an  electric-lighting  plant  where  but 
one  potential  is  in  use,  the  testing  potential  is  easily  obtained 
by  connecting  in  series  the  fine  wire  windings  of  two  or  three 
transformers  whose  coarse  wire  windings  are  connected  in  par- 
allel to  the  low-tension  mains. 

For  general  testing  work  a  regular  step-up  transformer  with 
a  spark  gauge  is  preferable. 

Transformer  Polarity. 

If  two  or  more  transformers  are  to  be  used,  connected  to- 
gether in  series  or  parallel,  it  is  necessary  to  know  the  relative 
instantaneous  directions  of  the  current  flow  in  each,  in  order 
that  they  may  not  oppose  each  other  in  the  first  case  or  short 
circuit  through  each  other  in  the  second.  For  making  this 
polarity  test  the  most  elementary  and  in  the  majority  of  cases 
the  most  satisfactory  method  is,  in  the  case  where  the  \levices 
are  connected  in  series,  to  make  this  series  connection  at  ran- 
dom, and  then  attach  a  voltmeter  to  the  free  terminals.  If  then 
the  connections  are  arranged  so  that  the  potentials  assist  each 
other,  the  voltmeter  will  show  double  the  voltage  indicated  by 
the  secondary  of  a  single  similar  transformer,  while  if  they  are 
connected  in  opposition  the  voltage  reading  will  be  zero. 
Where  the  secondaries  are  to  be  connected  in  parallel  this  may 
also  be  done  at  random,  fuses  being  inserted  between  them.  If 
when  the  primary  circuits  are  closed  the  fuses  blow,  the  con- 
nections are  such  that  the  transformers  are  short  circuited  on 
each  other.  If  they  remain  intact  the  coils  are  properly  con- 
nected in  parallel.  In  the  latter  test  the  capacity  of  the  fuses 
should  be  from  two  to  five  per  cent  of  the  full  load  capacity  of 
the  transformer  windings.  It  is  necessary  to  allow  a  margin 
as  transformers  are  never  exactly  alike,  and  there  is  always  a 
small  interchange  of  current  even  with  windings  properly 
paralleled. 

G-eneral. 

In  all  transformer  tests  it  is  advisable  to  place  in  series  with 
the  circuit  through  which  the  exciting  current  is  passed,  a  fuse 
rated  to  blow  at  about  50  per  cent  greater  current  than  the 
maximum  full  load  current  desired.  This  precaution  is  neces- 
sary, because  when  current  was  last  passed  through  the  trans- 
former it  has,  except  in  'the  very  rare  instance  in  which  it  was 


MISCELLANEOUS  DETERMINATIONS.  285 

interrupted  as  the  current  curve  passed  through  the  zero  value, 
been  cut  off  when  the  iron  core  was  magnetized  in  one  or  the 
other  direction.  If,  when  current  is  again  thrown  on,  the 
direction  of  the  initial  impulse  is  such  that  the  residual  magnet- 
ism of  the  core  tends  to  assist  instead  of  oppose  the  initial  rise 
in  current  strength  in  the  transformer  winding,  the  current  value 
may  rise  to  an  amount  so  greatly  in  excess  of  the  capacity  of 
the  measuring  instruments  that  the  needles  of  the  latter  will  be 
bent  or  the  movements  otherwise  damaged.  The  fuse  protec- 
tion will  generally  save  the  instruments  from  this  harm. 

TESTING   INTEGRATING   METERS. 

Integrating,  or  as  they  are  erroneously  but  more  commonly 
termed,  "  recording  "  instruments,  used  to  measure  the  amount 
of  power  supplied  to  a  consumer,  form  a  class  of  electrical 
measuring  apparatus  that  for  various  reasons  requires  frequent 
checking  to  determine  whether  or  not  the  accuracy  is  still 
within  permissible  limits. 

Test  with  Indicating  Instruments. 

A  common  method  of  testing  an  integrating  meter  consists  in 
connecting  in  circuit  with  it  an  instrument  of  the  indicating 
pattern  and  then  putting  on  a  steady  load  for  a  length  of  time 
measured  accurately  by  a  stop-watch.  The  integrating  instru- 
ment is  supposed  to  show  on  its  dials  the  ampere  hours  (or 
watt  hours,  as  the  case  may  be),  and  if  in  calibration  its  indica- 
tions should  of  course  correspond  with  the  ampere  (or  watt) 
hour  rate  figured  from  the  readings  of  the  indicating  apparatus 
and  the  watch.  The  meter  dials  are  seldom  sufficiently  sub- 
divided to  allow  of  an  accurate  reading  of  its  indication  unless 
the  test  is  extended  over  a  period  of  hours.  As  in  practically 
all  of  them,  however,  the  motion  of  the  moving  element  is 
reduced  through  a  train  of  gears,  it  is  possible  to  shorten  the 
time  of  the  test  by  observing  the  number  of  revolutions  made  by 
the  rotating  element  if  the  gear  reduction  ratio  is  known.  A 
paint  mark  on  the  rotating  part  makes  it  possible  to  count  the 
revolutions  accurately. 

Tests  made  with  portable  indicating  meters  have  the  great 
advantage  that  the  integrating  meter  may  thus  be  checked  in 
place  on  the  consumers'  premises,  the  load  being  adjusted  by 


286       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

switching  on  the  proper  number  of  lamps.  That  the  meter  is 
erected  at  the  point  where  it  is  to  be  when  doing  its  normal 
work  is  of  importance  for  accuracy,  as  well  as  convenience, 
since  all  such  devices  are  influenced  to  a  considerable  extent 
by  mechanical  vibrations,  and  a  meter  which  would  show  up  as 
correct  in  a  test  made  in  a  quiet  laboratory  might  register  wrongly 
when  erected  on  the  consumers'  premises.  Vibration  causes 
the  moving  element  to  jump  up  and  down  on  its  pivot,  and  the 
friction  in  this  case  is  well  known  to  be  less  than  the  friction 
existing  where  no  vibration  is  present.  The  error  is,  of  course, 
in  favor  of  the  supply  company  in  so  far  as  the  readings  are  apt 
to  be,  if  anything,  high,  but  on  the  other  hand  it  is  approaching 
too  closely  to  the  comic-paper  gas-meter  standard  if  the  appara- 
tus is  found  to  register  current  when  none  is  being  drawn  by 
the  consumer.  v 

The  test  in  place  with  indicating  instruments,  while  allowing 
for  some  of  the  peculiar  conditions  in  each  installation,  is  not 
always  feasible.  For  instance,  in  many  cases  the  load  on  the 
meter  is  not  steady  at  a  given  point  for  long  intervals,  but  with 
motor  loads,  and  particularly  when  these  motors  are  driving 
elevators,  is  fluctuating  violently  at  frequent  and  irregular 
intervals.  To  follow  the  ampere  fluctuations  with  an  ammeter 
or  the  watt  fluctuations  with  an  indicating  wattmeter  and  simul- 
taneously assign  the  correct  duration  period  to  each  by  referring 
to  a  stop-watch,  is  practically  impossible.  In  this  event  if  the 
current  is  continuous  it  is  advisable  to  resort  to  the  following 
scheme. 

Testing  with  Electrolytic  Meter. 

The  standard  in  this  case  becomes  a  voltammeter,  usually  of 
the  copper  pattern  described  on  page  14.  By  comparing  the  am- 
pere hours  as  shown  by  the  gain  in  weight  of  the  cathode  after 
being  in  circuit  for  any  desired  period  with  the  ampere  hours 
shown  by  the  dial  of  the  integrating  instrument,  the  accuracy  of 
the  latter  can  be  determined  offhand.  As  an  electrolytic  meter 
shows  the  product  of  the  true  average  current  by  the  time  that 
it  has  been  in  circuit,  results  of  a  high  degree  of  accuracy  may 
be  obtained  with  a  fair  chemical  balance  and  a  very  ordinary 
timepiece  if  the  period  over  which  the  test  extends  is  made 
reasonably  long. 


MISCELLANEOUS  DETERMINATIONS.  287 

If  the  integrating  meter  shows  watt  hours  instead  of  ampere 
hours  a  voltmeter  is  needed  in  addition  to  the  voltammeter,  and 
from  its  indications  it  is  necessary  to  derive  some  mean  volt 
value  which  will  fairly  represent  the  mean  voltage  during  the 
test.  The  volt  approximation  may  be  made  very  closely,  as  its 
extreme  fluctuations  are  usually  but  a  few  per  cent,  so  that  the 
average  can  be  ascertained  to  a  fraction  of  a  per  cent. 

Still  another  method  involves  the  use  of  a  regulation  motor 
type  integrating  meter  as  the  standard,  this  one  being  con- 
nected in  circuit  with  the  one  under  test,  so  that  the  attached 
load  is  simultaneously  measured  by  both.  The  readings  of  the 
two  must  obviously  agree  if  the  calibration  of  the  tested  one  is 
correct.  The  meter  used  as  the  standard  is  usually  specially 
constructed  so  as  to  obtain  maximum  accuracy.  The  gear  train 
and  dials  of  the  ordinary  meter  are  omitted  to  reduce  the  fric- 
tional  errors,  and  their  place  is  taken  by  a  pointer  attached 
directly  to  the  shaft  of  the  rotating  element  so  that  its  revolu- 
tion may  be  closely  observed.  The  bearings  are  often  made  of 
diamond  instead  of  sapphire,  and  particular  care  is  observed  in 
constructing  the  pivots  and  adjusting  the  calibration. 

Such  a  standard  must  itself  be  checked  from  time  to  time  by 
comparison  with  an  indicating  instrument  and  a  stop-watch,  but 
this  may  be  attended  to  at  the  station,  where  the  facilities  for 
such  work  are  better  than  on  the  consumers'  premises. 


CHAPTER    XII. 
THE  LOCATION  OF  FAULTS. 

IN  a  great  many  cases  electrical  measurements  may  be  made 
to  locate  electrical  faults,  which  measurements,  while  involving 
principles  that  have  been  mentioned  before  in  this  volume,  appear 
for  one  reason  or  another  somewhat  out  of  place  in  the  chapter 
setting  forth  their  said  principles. 

The  author  therefore  resorts  to  the  subterfuge  of  the  present 
"  miscellaneous  "  chapter  to  describe  and  discuss  the  more  com- 
mon and  useful  of  the  methods  which  can  be  included  itf  this 
convenient  category. 

While  it  gives  a  by  no  means  complete  list  of  the  numerous 
expedients  employed  in  various  of  the  more  specialized  methods 
of  testing,  it  is  thought  that  the  descriptions  taken  in  connec- 
tion with  what  has  gone  before  will  prove  of  assistance  in  figur- 
ing out  ways  and  means  of  locating  cases  of  electrical  trouble 
that  seem  to  be  somewhat  out  of  the  usual  run. 

One  of  the  most  common  and  often  at  the  same  time  the  most 
difficult  electrical  tests  that  has  to  be  made  is  for  the  location 
of  a  fault  in  a  conductor.  Such  faults  may  for  our  present 
purposes  conveniently  be  divided  into  two  classes,  the  first  being 
grounds  and  short  circuits,  and  the  second  complete  breaks 
or  open  circuits. 

LOCATION    OF    CROSSES    AND    GBOUNDSo 

If  the  fault  in  a  grounded  or  crossed  conductor  were  always 
of  practically  infinitely  low  resistance  —  that  is  to  say,  if  it  were 
a  "  dead  "  ground  or  short  circuit  —  its  location  could  easily  be 
detected  by  measuring  the  resistance  from  the  point  of  test  and 
back  again  through  the  ground  or  through  the  other  conductor 
affected,  by  any  of  the  Wheatstone  bridge  methods  described  in 
the  chapter  on  resistance  measurements.  Unfortunately,  how- 
ever, it  is  seldom  the  case  that  this  condition  exists,  and  tests 
giving  results  that  are  independent  of  the  resistance  of  the 


THE  LOCATION  OF  FAULTS.  289 

return  circuits  and  at  the  point  of  trouble  are  therefore  necessary. 
Another  very  frequent  source  of  inconvenience  and  error  lies  in 
the  fact  that  at  the  fault  there  may  exist  an  E.M.F.  due  in  some 
instances  to  the  contact  potential  difference  between  the  faulty 
conductor  and  that  on  which  it  is  grounded,  or  more  commonly, 
with  ground  return  circuits  such  as  telegraph  lines,  to  foreign 
earth  currents. 

In  the  majority  of  cases  it  is  possible  to  obtain  electrical  access 
to  both  ends  of  the  faulty  conductor.  If  this  is  a  cable  coiled 
up  in  a  tank  we  have  the  simplest  case,  as  the  two  ends  will, 
of  course,  be  close  together  and  may  be  carried  direct  to  the 
measuring  apparatus.  Where  the  fault  is  on  a  line  wire  or 
cable  it  is  almost  invariably  the  case  that  another  parallel  con- 
ductor that  is  not  faulty  is  available,  and  if  this  is  connected  to 
the  faulty  one  at  the  distant  station  a  loop  is  formed  whose 
terminals  are  adjacent  in  the  testing  station. 

Tests  which  require  that  access  be  had  to  both  terminals  of  a 
conductor  so  formed  are  called  "  loop  tests,"  the  most  prominent 
ones  being  the  following :  — 

The  Murray  L«op  Test. 

Referring  to  Fig.  229,  _Z?,  P,  E  is  the  looped  conductor,  B, 
P  being  the  outgoing  wire  having  a  fault  at  /,  and  P,  E  the 
return  wire  joined  to  the  former  at  the  distant  station  P.  This 
loop  is  used  to  form  one  side  of  a  Wheatetone  bridge,  the  two 
other  arms  of  the  bridge,  b  and  d,  being  formed  by  adjustable 
resistances  such  as  those  in  an  ordinary  post-office  pattern  test- 
ing set.  The  galvanometer  G-  and  battery  8  are  attached  as 
shown,  suitable  keys  Kl  and  K2  being  inserted  in  the  respective 
circuits.  Then,  as  is  the  case  in  the  ordinary  Wheatstone 
bridge,  a  resistance  in  the  battery  circuit  introduces  no  error  in 
the  result,  requiring  only  increased  battery  power  to  get  the 
same  sensibility.  This  resistance  in  the  Murray  test  is  that 
offered  by  the  earth  between  the  battery  terminals  and  the  fault 
plus  that  of  the  fault  itself.  In  making  measurements,  the 
resistances  in  b  and  d  are  first  made  equal  and  the  galvanometer 
key  K2  then  closed,  whereupon,  if  an  earth  current  is  present 
the  galvanometer  will  deflect  a  certain  amount,  which  should  be 
noted.  The  ratio  of  the  resistance  b  to  d  is  then  altered  until 
an  adjustment  is  reached  such  that  the  galvanometer  shows  the 


290        ELECTRIC  AND  MAGNETIC   MEASUREMENTS. 

same  deflection,  whether  K2  is  alone  depressed,  or  both  K1  and 
K2  are  depressed.  If  the  resistance  of  the  circuit  B,  P,  E,  which 
we  will  call  L,  is  known,  we  then  have  from  the  law  governing 

the  Wheatstone  bridge,  x=- The  resistance  of  B,P,E 

o  -f-  d 

is  measured  by  a  Wheatstone  bridge  in  the  ordinaiy  way. 

It  is  advisable  to  have  the  key  K1  of  a  special  reversing  type, 
so  that  when  one  of  its  buttons  is  depressed,  current  is  sent 
through  the  circuit  J.,  !S,  earth,  .F,  in  one  direction,  and  when 
the  other  is  depressed,  in  the  reverse  direction.  This  will 


Ground, 


FIG.  229. 


sometimes  give  slightly  different  results  for  the  two  connections, 
in  which  event  it  is  usually  safe  to  assume  that  their  mean  is 
the  correct  value.  If  the  results  differ  widely,  the  contacts 
should  be  examined  and  cleaned,  and  the  apparatus  should  be 
more  carefully  insulated  from  the  ground.  The  test  should  then 
be  repeated  until  concordant  results  are  obtained. 

Ohmmeter  Test. 

In  the  Murray  loop,  as  in  all  other  Wheatstone  bridge  tests,  the 
position  of  the  galvanometer  and  battery  in  the  network 
of  conductors  may  be  interchanged  without  affecting  the  results. 


THE  LOCATION  OF  FAULTS.  291 

The  ohmmeter  mentioned  on  page  107  may  be  used  for  this 
modification  of  the  Murray  test  by  making  connections  as  shown 
in  Fig.  230.  As  will  be  seen  from  this,  the  standard  resistance 
coil  forming  one  arm  of  a  Wheatstone  bridge  in  the  apparatus  is 
cut  out  of  use  by  withdrawing  the  connecting  plug  and  allowing 
it  to  hang  free.  The  middle  post  is  connected  to  ground,  and  the 
ends  of  the  looped  line  wire  are  attached  to  the  two  outer  posts. 
-The  stylus  is  tapped  along  the  wires  forming  the  ratio  arms  of 
the  bridge,  as  in  finding  a  resistance,  until  a  point  of  silence  is 
reached,  which  point  is  of  course  an  image  of  the  point  of 
trouble  on  the  line.  The  latter  can  then  be  located  by  reference 
to  the  equally  divided  scales  that  come  with  the  apparatus,  and 
which  show  the  result  in  percentage  of  the  total  line  length  in- 
cluded between  the  two  posts. 

The  result  so  found  is,  however,  correct  only  when  there  is 
no  difference  of  potential  between  the  grounded  wire  and  the 
grounded  'post  on  the  ohmmeter,  as  if  such  exists,  due  to  earth 


Ground' 

FIG.  230. 

currents  or  otherwise,  the  point  of  silence  on  the  bridge  wire  is 
not  the  image  of  the  fault,  but  a  false  one  corresponding  to  the 
false  result  that  would  be  obtained  if,  in  the  Murray  method 
above,  actual  galvanometer  zero  were  used  instead  of  the  false 
zero  obtained  on  depressing  the  key  Kl  alone.  The  human  ear 
is  unable  to  identify,  with  even  the  roughest  accuracy,  the  loud- 
ness  of  the  click  emitted  by  the  telephone  receiver,  and  there- 
fore if  the  ohmmeter  is  to  be  successfully  used  for  such  fault 
location  work,  it  must  be  provided  with  a  galvanometer  which 
can  be  switched  in  place  of  the  telephone  when  making  such 
readings,  and  the  work  done  from  a  false  zero,  as  in  the  ordinary 
Murray  method. 

The    Varley  Loop  Test. 

In  this,  as  in  the  Murray  test,  the   two  ends  of  the  faulty 
cable  must  be  made  accessible  by  forming  a  loop  with  it  and  a 


292       ELECTRIC   AND  MAGNETIC  MEASUREMENTS. 


good  return  conductor.  The  connections  are  then  to  be  made 
as  shown  in  Fig.  231,  from  which  it  will  be  seen  that  while  the 
bridge  arms,  the  galvanometer,  and  the  battery  are  arranged  as 
in  the  Murray  test,  a  resistance,  d,  has  been  inserted  between 
A  and  E.  The  arms  a  and  6,  of  constant  value  in  this  test,  are 
usually  made  equal  to  one  another,  and  d  is  adjustable  and 
varied  until  the  galvanometer  shows  the  same  deflection  whether 
its  key  K2  alone  is  closed  or  both  it  and  Kl  are  down  at  the 

b  L  —a  d 


same  time.     Under  these  circumstances  x  = 


b  -f  a 


In  the 


^VCuUjMA^J 


(rrouunds. 


FIG.  231. 


case  assumed  above,  i.e.,  when  b  =  a,  this  expression  becomes 

L-  d 
»--5— 

In  order  to  have  this  test  work  at  all  it  is  necessary  that  the 
fault  should  be  on  the  wire  that  is  connected  to  the  variable 
resistance  d,  because  if  it  is  not  no  balance  can  be  obtained. 

In  connection  with  the  Murray  and  Varley  loop  tests  de- 
scribed above,  the  distinction  between  earth  currents  and  those 
due  to  E.M.F.'s  set  up  at  the  fault  should  be  carefully  borne 
in  mind.  Earth  currents  are  possible  only  on  lines  a  part  of 


THE  LOCATION  OF  FAULTS.  293 

whose  circuit  is  formed  through  the  earth,  as  is  the  case  of  most 
telegraph  and  a  few  telephone  installations.  Contact  E.M.F.'s 
at  the  break  are,  on  the  other  hand,  present  both  in  ground 
return  lines  and  in  metallic  circuits.  As  will  be  noted  by  care- 
ful reference  to  Figs.  229  and  231,  a  deflection  of  the  galva- 
nometer will  be  given  when  its  key  is  closed  and  that  of  the 
battery  circuit  left  open  only  when  an  earth  current  exists,  and 
it  is  therefore  correct  to  use  the  false  zero  as  a  balancing  point 
only  with  grounded  circuits.  Where  earth  currents  are  absent, 
false  zeros  should  not  be  used  at  all,  and  if  there  is  a  galva- 
nometer deflection  when  the  galvanometer  key  is  closed  and  the 
battery  key  left  open,  it  shows  simply  that  there  is  leakage  from 
the  instrument  and  battery  itself  to  ground.  If  this  state  of 
affairs  exists,  the  leakage  should  be  stopped  by  carefully  clean- 
ing all  dirt  and  moisture  from  the  insulating  surfaces,  and  if 
necessary,  by  interposing  additional  resistances  in  the  shape  of 
porcelain  insulators. 

With  all  loop  tests  the  accuracy  is  greatest  with  a  high-resist- 
ance conductor.  While  telegraph  and  telephone  lines  have 
enough  resistance  to  enable  faults  to  be  located  with  a  sufficient 
degree  of  accuracy,  such  is  unfortunately  not  the  case  with  the 
heavy  wires  used  in  electric  light  plants.  The  errors  are  so 
large  as  to  make  the  results  perfectly  useless,  and  recourse 
must  therefore  be  had  to  other  methods. 

Induction  Method. 

This  is  one  that,  generally  speaking,  is  possible  with  alter- 
nating-current circuits  only.  It  consists  in  winding  up  of 
many  turns  of  wire  a  coil  that  is  made  as  large  as  possible  con- 
sistent with  portability,  and  is  carried  along  by  a  couple  of 
assistants  over  the  faulty  conductor  with  one  of  its  flat  sides 
parallel  thereto.  A  telephone  receiver  is  placed  in  the  circuit 
of  this  "  exploring  coil,"  and  as  long  as  alternating  current  is 
flowing  through  the  conductor,  the  current  induced  in  the 
exploring  winding  will  of  course  produce  a  loud  humming  noise 
in  the  receiver.  Referring  to  Fig.  232,  if  the  fault  /  is  at  B, 
the  observer  listening  to  the  receiver  when  the  exploring  coil  E 
is  being  carried  along  parallel  to  A,  C,  will  hear  a  note  until 
E  has  passed  B .  The  terminal  of  the  alternator  supplying 
current  to  the  good  conductor  must  of  course  be  grounded  at 


294      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

the   generating  station    in    order    that  current  may  flow  back 
through  the  ground  at  the  fault. 

This  test  is  beautifully  simple,  but  unfortunately  not  always 
applicable,  especially  under  the  conditions  where  buried  alter- 
nating mains  are  most  likely  to  be  used,  that  is,  in  densely  pop- 
ulated cities,  as  here  numerous  gas  and  other  metallic  pipes  are 
usually  present  and  the  conductor  may  itself  be  inclosed  in  a 
lead  sheathing,  all  of  which  so  modifies  the  tone  in  the  receiver 
that  instead  of  there  being  an  almost  abrupt  point  of  silence 
when  the  fault  is  reached,  the  noise  simply  decreases  slightly, 
and  it  is  very  difficult  to  say  just  where  this  occurs. 

Compass  Test. 

This  simple  and  remarkably  efficient  test  described  by  Mr. 
Stott  in  1901  is  available  for  the  location  of  grounds  not  only 
in  circuits  which  can  be  isolated  while  the  measurement  is  be- 


Telephone 
Receiver 


B 


Ground 


Ground, 

FIG.  232. 

ing  made,  but,  in  the  case  of  alternating-current  systems,  where 
the  conductor  is  in  use  as  well.  It  consists  in  sending  through 
the  faulty  wire,  the  fault  on  it  and  back  through  the  ground 
to  the  testing  station  a  direct  current  of  the  highest  convenient 
value.  The  direction  of  this  continuous  current  is  reversed  at 
known  and  approximately  equal  intervals  of,  say,  ten  seconds, 
by  means  of  a  commutator  that  is  driven  either  manually  or  by 
a  small  motor.  Referring  to  Fig.  233,  if  the  lower  of  the  two 
conductors  is  grounded  as  shown,  and  if  a  periodically  reversed 
direct  current  is  being  passed  through  the  conductor,  the  ground, 
and  back  to  the  test  station  by  the  aid  of  the  reversing  commu- 
tator indicated  in  the  figure,  the  needle  of  a  pocket  compass 
0  placed  parallel  to  the  faulty  main,  will  be  deflected  to  a 
position  nearly  at  right  angles  to  the  wire  in  one  direction 


THE  LOCATION  OF  FAULTS.  295 

until  the  continuous  current  is  reversed,  at  which  time  it  will 
jump  and  take  up  a  position  removed  nearly  180  degrees  from 
the  first  one.  If  the  wire  under  test  is  an  underground  conductor, 
the  compass  needle  can  be  laid  on  its  covering  at  each  successive 
manhole  until  one  is  found  where  these  periodical  reversals  of 
deflection  no  longer  exist.  The  ground  is  then  of  course  be- 
tween the  last  point  where  the  deflections  were  given  and  this 
one,  and  if  the  cable  is  tapped  at  the  former,  the  point  of  trouble 
will  usually  be  found  there.  In  any  event  it  has  been  located 
between  two  manholes,  which  is  all  that  is  usually  required  in 
practice,  as  if  it  exists  in  the  intervening  conductor,  the  cable 
must  be  pulled  out  of  the  ducts  anyway  in  order  to  effect  its 
desired  repair. 

The  alternating  current  flowing  through  the  main  B  does  not 
affect  the  compass  needle  appreciably,  as  the  rate  at  which  the 
alternations  take  place  is  so  much  greater  than  the  period  of 
oscillation  of  the  needle,  that  the  latter  either  does  not  move  at 


Ground, 
Orownoi 

FIG  .  233. 

all  or  else  simply  trembles  slightly,  and  has  a  motion  which  is 
negligible  as  compared  with  that  due  to  the  passage  of  the  con- 
tinuous test  current.  It  is  evidently  impossible  to  make  the 
same  test  with  direct  current  in  the  mains  J.,  B,  as  this  causes 
a  continued  deflection  of  the  needle  in  one  direction,  irrespective 
of  any  attempt  to  superimpose  on  it  a  reversed  current.  It  is 
however  possible  in  this  case  to  substitute  an  exploring  coil  arid 
telephone  receiver  for  the  compass  needle  and  an  alternating- 
current  generator  for  the  direct-current  source  with  its  reversing 
commutator  R,  but  the  current  delivered  by  the  d  c  machine 
must  be  sufficiently  smooth  to  avoid  producing  a  confusing  noise 
in  the  telephone  receiver.  The  current  delivered  by  a  Thomson- 
Houston  arc  machine  is  an  example  of  one  that  pulsates  suf- 
ficiently to  make  this  exploring  coil  test  out  of  the  question. 


296      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

Fall  of  Potential  Methods. 

An  elegant  method  of  locating  a  ground  in  a  faulty  conductor 
is  diagrammatical ly  illustrated  in  Fig.  234.  In  this  the  faulty 
conductor  is  the  line  B,  D ;  A,  B  being  a  length  of  good  con- 
ductor connected  in  series  with  and  preferably  located  parallel 
to  B,  I).  A  source  of  current  S,  usually  a  set  of  storage  bat- 
teries, is  used  to  cause  a  current  to  flow  through  the  circuit,  J., 
.B,/,  G-,  G-  as  shown,  and  an  ammeter  C  is  inserted  in  that  cir- 
cuit so  that  it  may  be  determined  that  the  current  strength  is 
kept  absolutely  constant.  If  now  we  know  the  resistance  of  A, 
B,  and  take  the  drop  in  potential  measured  by  a  galvanometer 
or  milli voltmeter  across  J.,  B,  and  B,  D,  respectively,  the 
resistance  of  the  faulty  cable  from  Btof  will  be  to  the  resist- 


B 


!?          c 


"'-===-   G  Grotmd, 

Ground 

FIG.  234. 

ance  of  the  good  cable  from  A  to  B,  as  the  deflection  due  to  the 
potential  drop  between  J5,  D,  is  to  the  deflection  given  when  the 
instrument  terminals  are  connected  to  J.,  D.  In  order  that 
the  resistance  of  the  galvanometer  leads  may  not  introduce  an 
error,  it  is  necessary  to  use  either  a  galvanometer  whose  resist- 
ance is  extremely  high  as  compared  with  that  of  R  and  X  in  the 
figure,  or  else,  which  amounts  to  the  same  thing,  to  have  it  of 
such  high  sensibility  that  a  large  resistance  may  be  inserted  in 
its  circuit.  If  a  section  of  conductor  running  parallel  to  B,  D, 
cannot  be  used  as  R,  a  low  resistance  can  of  course  be  used  in 
its  place,  but  this  plan  is  not  as  good,  as  the  temperature  of  the 
stretch  X  is  unknown,  and  if  it  differs  greatly  from  the  assumed 
70°  Fahr.,  on  which  its  resistance  measurement  is  based,  an  error 
equal  to  that  of  the  temperature  coefficient  of  copper,  that  is, 
two  tenths  of  a  per  cent  per  degree  Fahr.,  will  be  introduced. 
As  the  resistance  at  the  fault /is  often  variable,  it  is  most  con- 


THE  LOCATION  OF  FAULTS.  297 

venient  to  use  two  galvanometers  connected  to  the  points  A,  B, 
and  B,  D,  respectively,  both  graduated  in  known  fractions  of  a 

volt,    and    then  

observe  their  de-        A  B 

flections  simulta- 
neously.     If  this    ^^^^^^^^^^^^^^^^^^^^^g 
cannot  be    done, 

a    single    instru-  FlG- 235- 

ment  and  a  switch  for  shifting  the  connections  rapidly  should 
be  used,  a  careful  watch  being  kept  on  the  ammeter  to  be  sure 
that  the  current  has  not  changed,  as  on  its  having  the  same  value 
during  both  readings  depends  the  accuracy  of  the  result. 

Location  of  Crosses. 

Crosses  are  simply  the  grounding  of  one  conductor  on  another, 
and  may  be  located  in  exactly  the  same  way  that  grounds  are 
located,  as  described  above,  if  the  wire  with  which  the  cross  has 
been  made  is  substituted  for  the  earth  circuit  in  the  ground 
tests.  The  localization  of  crosses  is  usually  a  more  simple  test 
than  with  grounded  circuits,  as  the  question  of  earth  currents  is 
entirely  eliminated,  and  E.M.F.'s  at  the  point  of  contact  are  of 
less  common  occurrence. 

Location  of  Breaks. 

Where  a  conductor  is  actually  broken,  and  the  return  circuit 
from  the  break  is  therefore  of  a  resistance  that  is  practically  in- 
finitely high,  we  are  confronted  with  a  new  set  of  conditions. 

Whether  the  conductor  is  an  aerial  one  or  whether  it  is  a  cable 
buried  in  the  earth  or  submerged  in  water,  it  may  be  considered 
as  one  coating  of  a  condenser,  the  dielectric  being  the  insulation 
from  the  point  of  test  to  the  break,  and  the  other  coating  being 
the  earth  or  the  surrounding  water,  as  the  case  may  be.  The 
capacity  of  the  condenser  so  formed  may  be  measured  by  any  of 
the  methods  of  capacity  measurement  mentioned  in  Chapter  VIII, 
and  if  this  capacity  is  compared  with  that  of  a  neighboring  good 
conductor  whose  length  to  the  distant  station  B,  Fig.  235,  is 
known,  the  location  of  the  fault /is  given  directly  by  the  ratio 
of  the  capacities.  Where  no  apparatus  capable  of  measuring 
capacity  in  microfarads  is  available  the  fault  may  still  be  lo- 
cated by  simple  comparison  of  the  capacity  of  A,  f  with  that  of 


298      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

the  good  conductor  A,  B.  The  already  much  described  ohmmeter 
can  be  used  for  this  test  to  advantage,  the  connections  being  as 
in  Fig.  236.  In  this  test  it  is  necessary  that  the  potential  ap- 
plied to  the  bridge  wire  terminals  be  an  alternating  one  which 
may  conveniently  be  obtained  from  the  secondary  of  an  induc- 


FlG.  236. 


tion  coil.  The  point  of  silence  on  the  bridge  wire  is  then  one 
which  divides  up  the  total  bridge  wire  length  into  two  sections 
which  are  to  each  other  as  the  capacities  of  the  broken  and  good 
conductors. 

This  ohmmeter  test  can  be  used  only  under  favorable  condi- 


Telephone 


r^         r 

if     i 

1  I 

JS^        - 

4                 f 

gj—i 

'  1                                                   R 

-       J 

fe     ] 

1 

*=> 
<=> 

d> 

FIG.  237. 


tions,  as  the  resistance  of  the  slide  wire  is  but  small,  and  while  it  is 
without  capacity  has  a  small  self-induction  due  to  the  fact  that 
the  wire  forms  a  loop.  A  device  for  the  location  of  breaks  that 


THE  LOCATION  OF  FAULTS. 


299 


depends  on  a  somewhat  different  principle  and  which  is  appli- 
cable to  a  greater  variety  of  cases  is  the  Meyers  break  finder 
illustrated  diagrammatically  in  Fig.  237  and  in  perspective  in  Fig. 
238.  In  this  the  secondary  of  an  induction  coil  wound  as  a 
long  spool  has  its  terminals  attached  to  the  ends  of  the  faulty 
and  good  wires  respectively,  and  a  narrow  primary  coil  winding 
is  arranged  to  slide  up  and  down  along  the  secondary. 

Simple  inspection  of  the  figure  will  show  that  the  primary  may 


M 


FIG.  238. 

be  moved  to  a  position  such  that  a  telephone  receiver  connected 
across  the  secondary  terminals  will  cease  to  emit  a  hum,  and 
that  if  an  index  attached  to  the  primary  moves  over  a  scale,  the 
scale  may  be  divided  so  that  the  ratio  of  the  capacity  of  the  good 
to  the  broken  conductor  and  hence  the  ratio  of  the  length  of 
the  good  conductor  to  that  of  the  faulty  one  up  to  the  break 
will  be  shown  directly. 

AKMATURE    TESTING. 

One  of  the  most  common  tests  that  has  to  be  made  under 
commercial  conditions  is  the  location  of  a  fault  in  the  armature 
of  a  generator  or  motor.  The  extent  and  nature  of  the  discol- 


300      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

oration  of  the  commutator  bars  will  sometimes  give  an  indica- 
tion of  the  nature  of  the  difficulty  if  the  machine  has  been  in 
operation,  but  the  trouble  may  be  more  surely  located  by  calling 
in  the  aid  of  measuring  apparatus. 

Electrical  faults  in  the  windings  of  an  armature  consist  either 
of  a  ground  between  the  winding  and  the  iron  core,  or  of  a  wholly 
or  partially  short-circuited  section,  or  of  a  section  that  is  of  high 
resistance  or  all-together  opened. 

Testing  for   Grounds. 

The  fact  that  a  ground  exists  in  an  armature  is  easily  deter- 
mined in  a  dozen  different  ways,  one  of  the  simplest  being  to 


FIG.  239. 

pass  current  from  an  outside  source  through  an  incandescent 
lamp  in  series  with  which  there  is  placed  the  suspected  arma- 
ture, one  wire  being  attached  to  the  shaft  and  the  other  to  the 
commutator  bars.  If  the  lamp  lights,  there  is  of  course  elec- 
trical contact  between  the  windings  and  the  shaft.  If  this  or 
any  other  method  shows  that  a  ground  exists,  it  may  be  located 
as  follows :  Referring  to  Fig.  239,  current  is  passed  from  the 


THE  LOCATION  OF  FAULTS.  301 

shaft  through  the  ground  and  back  to  the  commutator  by  means 
of  conductors  attached  to  one  brush  and  to  the  shaft  respec- 
tively. The  current  may  be  taken  from  a  convenient  electric- 
light  main,  an  incandescent  lamp  being  interposed  to  prevent  an 
excessive  flow.  A  galvanometer,  which  in  central  stations  may 
conveniently  be  a  switchboard  ammeter  of  the  shunt  type  with 
its  shunt  disconnected,  is  then  attached  so  that  one  terminal  is 
on  the  shaft  and  the  other  free  to  be  moved  around  the  commu- 
tator. If  the  ground  is  at  that  point  of  the  winding  designated 
by  the  cross  in  the  figure,  the  deflection  of  the  galvanometer  will 
be  a  minimum  when  its  terminals  rest  on  the  commutator  bar 
to  which  that  lead  is  attached.  If  the  ground  were  midway  be- 
tween the  terminals  attached  to  two  adjacent  commutator  bars, 
the  deflection  at  these  two  bars  would  be  alike  and  both  would 
be  less  than  that  given  at  any  other  point  on  the  commutator. 
All  that  is  usually  desired  is  to  know  which  coil  the  ground  is 
in,  but  this  feature  enables  one  to  tell  approximately  at  what 
point  on  the  length  of  the  coil  the  ground  is  located  as  well  by 
observing  the  magnitude  of  the  deflection  given  when  the  gal- 
vanometer terminal  is  on  the  two  adjoining  commutator  bars. 

Location  of  Crosses. 

Current  is  passed  through  the  armature  under  test  through 
two  of  its  sets  of  brushes,  these  two  being  usually  selected  so  as 
to  be  diametrically  opposite.  The  current  is  taken  from  another 
main,  as  in  the  preceding  test.  Terminals  from  a  galvanometer, 
which  may  likewise  be  a  shunt  type  ammeter  without  its  shunt, 
are  then  placed  on  adjacent  commutator  bars,  as  shown  in  Fig. 
240,  and  the  deflection  noted.  This  operation  is  repeated  around 
the  whole  circumference  of  the  commutator,  bar  by  bar,  and  the 
deflections  will  all  be  alike  (if  the  strength  of  the  current  flow- 
ing through  the  armature  is  kept  constant),  until  the  bars  to 
which  the  ends  of  the  defective  coil  are  attached  are  reached, 
whereupon  the  deflection  will  naturally  be  less  as  the  current, 
instead  of  being  obliged  to  flow  through  the  full  length  of  the 
coil,  then  shunts  part  of  it  through  the  short  circuit.  This  is 
usually  called  the  "  bar  to  bar  test." 

In  making  the  above  test,  it  must  be  borne  in  mind  that  any 
decrease  in  the  strength  of  the  current  through  the  armature 
means  a  decrease  in  drop  between  adjacent  bars.  When  testing 


302      ELECTRIC  AND   MAGNETIC  MEASUREMENTS. 

on  a  fairly  steady  circuit,  it  is  usually  sufficient  to  place  an  am- 
meter in  the  supply  line  and  see  that  the  current  does  not  change 
too  greatly. 

When  the  current  is  taken  from  a  source  like  a  street  railway 
line,  however,  where  the  E.M.F.  is  constantly  varying  over  a 
wide  range,  it  is  better  to  use  either  two  separate  millivoltme- 
ters  or  a  combination  one  like  that  mentioned  on  page  129.  By 
using  a  separate  armature  coil  known  to  be  perfect,  or  even  a 
length  of  the  wire  leads  to  the  armature  of  equivalent  resist- 
ance, as  a  shunt  to  one  instrument,  the  other  instrument  will 
give  the  same  reading  when  its  terminals  are  touched  to  the 
adjacent  segments  of  a  good  coil  and  a  lesser  one  for  a  short- 


FIG.  240. 

circuited  coiL     The  deflections  may  vary  at  different  times,  but 
as  long  as  they  are  alike  the  coil  under  test  is  known  to  be  good, 

Location  of  Open  Circuits. 

For  locating  open-circuited  coils  connections  are  made  ex- 
actly as  shown  in  Fig.  240,  but  the  strength  of  the  current  passed 
through  the  armature  is  decreased  or  the  galvanometer  sensibil- 
ity made  less  by  inserting  a  resistance  in  series  with  it  or  a  shunt 
across  its  terminals.  No  deflection  will  be  given  as  the  galva- 
nometer terminals  are  carried  from  each  adjacent  commutator  bar 
pair  to  the  next  until  those  two  are  reached  between  which  the 
open  circuit  exists.  At  this  point  there  will  be  an  electromotive 
force  equal  to  the  total  drop  between  the  two  brushes,  and  the 
galvanometer  needle  will  be  violently  deflected. 


THE  LOCATION  OF  FAULTS.  SOS 

Location  of  Reversed  Coils. 

A  coil  whose  connection  to  the  commutator  bars  is  the  reverse 
of  the  proper  one  is  a  rare  occurrence,  but  it  sometimes  happens 
that  in  winding  an  armature  this  mistake  is  made.  If  the  arma- 
ture is  tested  by  the  bar  to  bar  method  above  described,  a  re- 
versed coil  is  detected  at  once  when  the  galvanometer  terminals 
are  applied,  as  the  needle  will  swing  in  a  direction  opposite  to 
that  which  it  took  with  all  the  other  and  properly  connected 
coils. 

Coil  Resistances. 

If  the  strength  of  the  current  that  is  being  passed  through  an 
armature  is  known  by  inserting  an  ammeter  in  that  circuit,  and 
if  the  galvanometer  is  calibrated  in  millivolts,  the  bar  to  bar 
test  will  give  the  actual  coil  resistance  in  ohms  by  simple  cal- 
culation, using  Ohm's  law.  In  making  such  calculations  the 
armature  connections  must  be  borne  in  mind,  as  the  current 
through  a  good  armature  flows  always  through  two  and  often 
through  more  branches  of  equal  resistance  connected  in  parallel, 
so  that  the  current  shown  by  the  ammeter  must  be  accordingly 
reckoned  per  coil. 


PART   II. 


CHAPTER  I. 

RECORDING   INSTRUMENTS. 

THE  phrase  "  recording  instruments"  is  often  used  to  designate 
an  integrating  instrument  whose  indications  show  the  product  of 
the  average  current  or  wattage  by  time,  but  the  term  is  incorrect 
in  this  sense,  as  it  actually  has  reference  to  an  instrument  in 
which  some  marking  device  inscribes  on  a  record  chart  a  line 
showing  the  instantaneous  values  of  voltage,  potential,  current, 
or  power,  at  all  times.  Such  recording  instruments  are  also 
called  registering  instruments. 

The  principle  on  which  such  devices  are  based  permits  of 
dividing  them  into  three  general  classes :  the  first  is  that  in 
which  an  ordinary  indicating  instrument  of  any  of  the  types 
heretofore  described  has  attached  to  its  needle  a  marking  pen 
or  pencil  which  moves  over  a  chart  that  is  being  continuously 
pulled  forward  by  clockwork ;  the  second  class  takes  in  those 
recorders  in  which  there  is  likewise  used  an  indicating  instrument 
mechanism,  but  whose  needle  is  free  to  move  and  take  up  any 
desired  position,  a  device  being  attached  through  whose  aid  the 
needle  positions  are  marked  on  a  clockwork-driven  chart  at  regu- 
lar intervals ;  the  third  class  of  recorders  might  be  termed  "  relay 
recorders,"  in  which  the  mechanism  of  an  indicating  instrument 
actuates  a  marking  device,  not  directly,  but  through  relays 
which  control  some  source  of  mechanical  power  of  relatively 
great  strength. 

RECORDERS    OF    THE    FIRST    CLASS. 

Bristol  Recorders. 

The  simplest  of  the  recorders  of  the  first  class  made  in  this 
country  is  the  Bristol  instrument  illustrated  in  Fig.  241.  In  it 
the  chart  takes  the  form  of  a  paper  disk,  which  is  rotated  by  clock- 

304 


RECORDING  INSTRUMENTS. 


305 


work  at  an  appropriate  rate.  The  instrument  mechanism  consists 
of  a  solenoid  voltmeter  or  ammeter  whose  main  winding  is  a  coil 
whose  axis  is  placed  horizontally,  and  whose  core  actuates  the 
upper  end  of  the  needle  shown,  the  force  opposing  the  motion 
of  the  needle  being  the  elasticity  of  its  lower  flat  spring  end. 
The  upper  end  of  the  needle  carries  a  V-shaped  trough  in  which 
there  is  placed  a  drop  or  two  of  slow-drying  glycerine  aniline  ink 
which  is  drawn  to  the  end  of  the  trough  by  capillary  attraction 
and  so  makes  a  fine  line  on  the  paper. 

Aside  from  the  fact  that  the  charts  on  such  instruments  are 
unsatisfactory  because  the  ab- 
scissa and  ordinates  are  not 
straight  lines  crossing  at  right 
angles,  but  circle  arcs,  so  that 
the  records  are  difficult  to  in- 
terpret and  practically  impos- 
sible to  integrate  with  a  plani- 
meter,  the  friction  between  the 
pen  and  the  paper  is  so  great 
as  compared  with  the  power 
exerted  by  the  instrument  mech- 
anism that  a  considerable 
change  in  load  must  take  place 
before  the  pen  will  move,  and 
even  then  it  may  take  up  a 
position  which  does  not  accu- 
rately indicate  the  new  value. 
The  error  due  to  this  friction 
may  easily  be  in  excess  of  5 
per  cent. 


FIG.  241. 


Chauvin  and  Arnoux  Recorders. 

An  ingenious  device  for  partially  eliminating  the  above- 
mentioned  friction  errors  is  used  on  the  recording  instru- 
ment made  by  Chauvin  and  Arnoux,  of  Paris.  This  consists 
of  an  ink  roller  which  is  attached  to  the  end  of  a  needle 
actuated  by  an  enlarged  specimen  of  an  ordinary  indicating 
instrument  movement,  the  roller  being  shown  in  Fig.  242. 
It  consists  of  two  halves,  A  and  B,  the  former  of  which 
is  open  above  and  below  and  the  latter  above  only.  A 


306       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


lenticular  piece  of  porous  porcelain  or  a  disk  of  blotting  paper 
is  placed  between  A  and  B  and  the  two  then  screwed  together 
by  an  appropriate  thread,  so  that  only  a  very  fine  gap  is  left 

between  them.  Both  the  upper 
end  of  A  and  the  lower  end  of 
B  are  provided  with  small  jew- 
eled bearings  which  in  turn  rest 
on  pivots,  both  of  the  pivots 
being  secured  to  the  pen  frame, 
f  F.  This  leaves  the  roller  free 
to  rotate  about  its  axis.  A  drop 
of  alcohol  is  first  allowed  to  fall 
into  the  open  end  of  A,  and  this 
moistens  the  porous  washer  and 
tends  to  flow  outward  through 
the  crevice  between  A  and  B. 


FIG.  242. 


Aniline  ink  is  put  into  A  imme- 
\       diately  after,  and   this  follows 

the  course  of  the  alcohol,  so 
that  the  ink  is  drawn  to  the  edge  and  will  of  course  make  a 
mark  on  the  paper  chart  rotated  at  right  angles  to  and  in  contact 
with  it.  A  complete  Chauvin  and  Arnoux  recorder  having  an 
actuating  mechanism  of  the  hot  wire  indicating  instrument 
pattern  is  shown  in  Fig.  243,  which  cut  will  make  the  method  of 
attaching  the  pen  more  clear. 

This  rolling  pen  reduces  the  friction  between  the  marking 
device  and  the  chart  very  materially,  but  it  makes  rather  a  broad 
line,  so  that  it  is  difficult  to  detect  minute  changes  by  inspection 
of  the  record  curve. 

Creneral  ^Electric   Co.  Recorder. 

Strictly  speaking,  this  also  is  a  recorder  in  which  the  records 
are  obtained  by  attaching  to  the  extremity  of  the  needle  of  an 
indicating  pattern  instrument  a  pen,  which  by  its  travels  over 
the  surface  of  a  paper  chart  carried  beneath  it  by  means  of 
clockwork,  traces  a  curve  showing  the  variations  in  current 
strength.  The  problem  of  eliminating  the  frictional  errors  due 
to  the  friction  of  the  pen  on  the  record  sheet  has  in  this  device 
been  attacked  by  an  endeavor  to  make  the  torque  of  the  moving 
system  so  high  that  the  frictional  retarding  forces  form  but  an 


RECORDING  INSTRUMENTS. 


307 


inappreciable  percentage  thereof.  One  of  the  expedients 
involved  is  the  reduction  of  the  angular  motion  of  the  needle 
to  about  20°  in  place  of  the  conventional  80°  or  90°.  This  of 
itself  brings  about  a  quadrupling  of  the  effort  exerted  for  a 
given  percentage  change  in  load,  although  it  involves,  too, 
chart  ordinates  which  are  very  short.  A  still  further  increase 
in  the  power  for  actuating  the  recording  pen  is  obtained  as 
follows:  The  measuring  instrument  portion  of  the  apparatus 
is  that  of  the  conventional  d'Arsonval  meter  kinematically 
inverted,  that  is  to  say,  the 
moving  coil  carries  a  steady 
current  of  the  maximum 
strength  permitted  by  the 
design  and  swings  in  a  mag- 
netic field  whose  intensity 
varies  with  the  load  to  be 
measured,  in  place  of  having 
the  coil  current  the  variable 
and  the  field  strength  fixed 
at  the  maximum  that  the 
design  allows. 

There  is  thus  a  moving 
coil  whose  windings  carry  a 
constant,  uniform  current 
from  some  separate  source 
and  stationary  coils  furnish- 
ing the  field  in  which  the 
movable  one  swings.  The 
plan  necessitates  the  compli- 
cation of  a  set  of  storage 
batteries  to  supply  the  mov- 
ing coil  current  and  an  in- 
dicating instrument  in  that  battery  line  to  show  that  the  cur- 
rent strength  remains  unchanged,  but  has  the  advantage  that 
the  current  from  the  source  to  be  measured  may  be  of  almost 
any  value  as  it  flows  through  stationary  windings,  and  'here 
are  hence  no  difficulties  because  of  the  limited  current  capacity 
of  springs  or  the  like.  Excellent  damping  qualities  result  also, 
owing  to  the  intensity  of  the  field  in  which  the  coil  swings. 

A  General  Electric  recording  ammeter  is  shown  in  Fig.  244, 


FIG.  243. 


308       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

where  the  indicating  instrument  relied  upon  to  show  that  the 
strength  of  the  current  through  the  movable  coil  windings 
remains  unchanged,  is  likewise  visible.  The  same  clockwork 
that  draws  the.  band  of  paper  along  under  the  marking  pen 
makes  marks  on  the  chart  at  regular  time  intervals,  from  which 
marks  the  elapsed  time  may  thus  be  read  off. 

While  heavy,  cumbersome,  and  costly,  the  apparatus  forms 
probably  the  best  means  available  to-day  for  obtaining  con- 
tinuous records  of  rapidly  fluctuating  loads  within  its  capacity, 


FIG.  244. 

being  specially  valuable  for  such  work  as  the  plotting  of  the 
current  input  curves  of  elevator  and  street  railway  motors. 

RECORDERS    OF    THE    SECOND    CLASS. 
Grans  and  Croldschmidt  Instrument. 

In  this  device  the  clockwork  and  paper  drum  arrangement  is 
much  the  same  as  in  the  Chauvin  and  Arnoux  recorders,  but 
the  pen  carried  by  the  indicating  instrument  is  not  kept  in 
constant  contact  with  the  paper.  As  can  be  seen  from 
Fig.  245,  a  curved  arm  extends  across  the  scale  and  above  the 


RECORDING  INSTRUMENTS. 


309 


needle.  This  arm  is  sharply  knocked  down  toward  the  paper 
at  regular  intervals,  controlled  by  a  clock,  and  as  this  happens, 
the  marker  attached  to  the  indicating  needle  is  likewise  ham- 
mered against  the  paper,  so  that  registry  of  a  number  of  individual 
indications  is  made  and  conveys  practically  the  same  information 
as  if  the  record  of  the  meter  were  a  continuous  one. 

This  type  of  instrument  is  attractive  on  account  of  the  fact 
that  the  mechanism  actuated  by  the  current  may  be  of  the  con- 
ventional indicating  instrument  power  and  design,  for,  being 
entirely  unhampered  in  its  motion,  except  at  the  instants  when 
it  is  struck  by  the  striker  bar,  the  needle  swings  as  freely  as 
that  of  an  indicating  device.  The  periodic  arresting  of  needle 
motion  is,  if  anything,  rather  an  advantage  in  so  far  as  these 


FIG.  245. 

checks  serve  to  prevent  the  needle  of  otherwise  poorly  damped 
apparatus  from  swinging  about  too  violently.  The  apparatus 
is  not  satisfactory  on  a  rapidly  fluctuating  load,  as  the  striker 
bar  does  not  work  with  a  rapidity  sufficient  to  cause  the  suc- 
cessive dots  on  the  chart  to  follow  one  another  closely  enough 
to  give  an  approximation  to  a  continuous  line  under  the 
circumstances. 

No  meters  of  the  type  are  made  in  this  country,  but  they  are 
in  limited  use  abroad,  particularly  for  recording  the  deflection 
of  instruments  with  low  torques  like  galvanometers. 


310       ELECTRIC  AND   MAGNETIC  MEASUREMENTS. 
RECORDERS    OF   THE   THIRD    CLASS. 

The    Callendar  Recorder. 

One  of  the  earliest  relay  recorders  is  the  Callendar  instrument, 
which  is  primarily  a  recording  slide-wire  bridge.  Fig.  246  shows 
its  method  of  operation.  In  that  figure  MN  is  the  straight 
stretched  wire  of  an  ordinary  slide-wire  bridge,  the  standard  and 
unknown  resistances  being  inserted  in  the  usual  way,  as  likewise 
are  the  battery  and  galvanometer  circuits.  The  sliding  contact 
on  S  slides  along  a  bar,  and  is  pulled  toward  MOT  JV,  as  the  case 
may  be,  by  the  endless  cord  shown  passing  over  the  idle  pulleys, 
Z>Z>,  and  making  a  turn  around  the  drum,  P.  The  galvanometer 
is  special,  in  that  when  it  deflects  because  the  bridge  circuits  are 
unbalanced  its  needle  comes  against  one  of  the  other  of  the 


Goto. 


FIG.  246. 


stops  E  and  F.  When  it  is  against  E,  a  circuit  which  can  be 
traced  out  from  the  figure  is  closed,  and  this  energizes  an 
electromagnet,  I.  This  magnet  pulls  down  one  end  of  a 
lever,  and  in  so  doing  raises  the  other  end,  which  is  a  brake 
that  prevents  the  gear  wheel,  R,  from  turning.  As  R  then 
rotates,  it  in  turn  actuates  the  pinion,  B,  which  latter  rotates  the 
drum,  P,  and  pulls  the  sliding  contact  in  the  direction  that  it 
must  be  moved  in  order  to  restore  the  balance.  If  the  galvano- 
meter needle  touched  P  instead,  the  pinion,  J.,  would  be  actuated, 
and  the  drum,  P,  would  pull  the  sliding  contact  in  the  opposite 
direction.  The  manner  in  which  the  drum,  P,  is  caused  to 
rotate  in  one  direction  or  the  other,  according  as  B  or  A  is  turn- 
ing, is  best  seen  from  Fig.  247,  which  shows  an  enlarged  view 
of  this  mechanical  appliance.  Q  is  a  stationary  shaft  on  which 


RECORDING  INSTRUMENTS.  311 

a  gear  wheel,  K,  may  rotate  freely.  This  wheel  and  its  mate,  L, 
are  provided  with  both  spur  and  bevel  teeth.  L  is  free  to 
rotate  on  the  outer  surface  of  the  shaft,  T,  carrying  the  drum,  P. 
Fastened  at  right  angles  to  T  is  an  arm,  £7,  on  which  there  rotates 
the  bevel  pinion,  V.  If  A  and  therefore  K  are  stationary,  and 
B  rotates,  L  will  evidently  be  revolved  about  I7  and  in  so  doing 
will  not  only  rotate  V  about  its  axis,  C7,  but  will  carry  U  around 
the  shaft,  Q.  In  like  manner,  if  B  and  hence  L  are  stationary, 
and  A  rotates,  K  will  rotate  U  about  Q  in  the  opposite  direc- 


FIG.  247. 

tion.  If  both  A  and  B  were  released  from  the  control  of  their 
brakes  simultaneously,  as  would  practically  be  the  case  if  the 
galvanometer  were  subjected  to  heavy  mechanical  vibration  so 
that  it  tapped  E  and  F  in  rapid  succession,  V  would  rotate 
about  £/",  but  U  would  not  rotate  T  around  Q.  This  device  is 
like  the  balance  gear  used  on  automobiles. 

The  power  for  driving  A  and  B  is  obtained  from  a  pair  of 
independent  clockworks.  A  pen  carried  by  the  arm  that  sup- 
ports the  sliding  contact,  on  S,  is  drawn  backward  and  forward 
on  the  record  paper  by  it,  and  so  makes  the  desired  chart. 


312       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

While  the  instrument  as  described  is  e,  recording  bridge  giving 
a  record  of  any  changes  in  the  value  of  resistance,  Jf,  it  can,  as  is 
evident  from  the  chapter  on  slide-wire  bridges,  easily  be  modified 
to  become  a  recording  potentiometer,  in  which  case  it  will  give 
records  of  potentials,  currents,  temperatures,  etc. 

The  Arconi  Recorder. 

In  this  device  the  needle  of  an  indicating  instrument  actuates, 
as  is  shown  in  Fig.  248,  a  contact  which  comes  against  one  or 


FIG.  248. 


the  other  of  the  stops  A  and  B  when  the  value  of  the  current 
flowing  through  the  instrument  changes.  A  motor,  M,  is  set  in 
rotation  when  the  needle  is  in  contact  with  either  stop  by  com- 
pleting the  circuit  through  the  motor  armature,  and  revolves  in 


RECORDING  INSTRUMENTS. 


313 


one  direction  with  the  contact  on  ^4,  and  in  the  reverse  direction 
when  it  is  on  B.  The  torque  exerted  by  the  instrument  needle 
is  opposed  by  that  of  the  coiled  spring,  S,  and  the  free  end  of 
that  spring  is  attached  to  a  carriage  that  is  driven  by  the  motor. 


FIG.  249. 

The  connections  are  such  that  when  the  current  strength 
increases  the  needle  makes  the  contact  for  that  circuit  wLich 
will  revolve  the  motor  armature,  and  hence  move  the  spring 
terminal  in  such  a  way  as  to  increase  the  spring  tension.  The 
motor  will  of  course  be  kept  on  rotating  until  this  increased 
tension  is  sufficient  to  pull  the  needle  away  from  its  stop, 


314      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


whereupon  the  circuit  is  broken  and  the  motor  comes  to  rest. 
A  pen,  JP,  is  attached  to  the  rack  that  is  moved  by  the  motor 
and  traces  on  the  chart  the  varying  positions  that  the  rack  has 
assumed  and  which  show  the  measures  of  the  current  strength. 

The  indicating  instrument  mechanism  may  obviously  be  either 
a  voltmeter,  ammeter,  or  a  wattmeter,  according  to  the  quantity 
that  it  is  desired  to  observe. 

A  complete  instrument  of  this  kind  is  illustrated  in  Fig.  249. 

The    Weston  Recorder. 

This  device  is  similar  to  the  Arconi  recorder,  in  that  an 
indicating  instrument  mechanism  causes  the  direction  of  rotation 


FIG.  250. 

of  an  electric  motor  to  reverse  according  as  the  needle  deflects 
against  one  or  the  other  of  a  pair  of  stops,  and  in  that  the  pen 
that  makes  the  record  on  the  chart  is  moved  back  and  forth  by 
the  motor.  Instead,  however,  of  varying  the  magnitude  of  the 
torque  resisting  the  swing  of  the  needle  by  the  position  of  the 
recorder  carriage,  the  torque  actuating  the  needle  is  varied  by 
varying  a  resistance  placed  in  series  with  the  indicating  mechan- 
ism. A  diagrammatic  illustration  of  this  device  is  shown  in 
Fig.  250,  and  will  be  understood  without  further  explanation. 

Another  form  of  Weston  recorder  is  that  illustrated  in 
Fig.  251.  In  this  neither  the  torque  of  the  indicating  needle  nor 
that  of  the  spring  opposing  its  motion  is  varied,  but  the  position 


RE-CORDING  INSTRUMENTS. 


315 


of  the  stop  contacts  is  changed  instead.  As  is  shown  by  the 
figure,  the  stops  are  carried  on  a  frame  mounted  co-axially  with 
the  indicating  mechanism,  and  are  caused  to  rotate  by  a  motor 
which  drives  their  frame  through  gears.  The  direction  of  the 
rotation  of  the  motor  is  determined  by  the  pair  of  stops  with 
which  the  needle  is  in  contact,  and  it  carries  the  frame  with  the 
contacts  along,  until  the  circuit  is  broken  and  the  needle  left 
free.  The  recording  pen  is  driven  back  and  forth  on  its  chart 
by  the  motor. 

Boyle's  Recorder. 

This  piece  of  apparatus  is  diagrammatically  illustrated  in 
Fig.  252.  It  employs  an  ordinary  indicating  instrument  mech- 
anism, J,  on  which  there  is  a  needle  with  a  contact  point  at 
its  end,  as  in  the  apparatus  above.  The  stops  against  which 
this  contact  plays  are,  however,  not  stationary,  but  composed  of 
two  plates,  8  and  jP,  insulated  from  one  another  but  mechani- 
cally secured  to  a  com- 
mon framework  and 
in  rigid  connection 
with  a  piston,  P,  mov- 
ing in  a  cylinder. 
When  the  needle 
makes  contact  with  one 
of  the  plates,  say  $,  a 
circuit  is  closed  through 
a  local  battery  and  S, 
and  through  two 
electrically  controlled 
valves,  E1,  E\  When 
current  flows  through 
the  valve  windings 
both  are  opened.  As 
will  be  seen  from  the 
figure,  this  with  the 

piping  arrangement  shown  will  admit  water  that  is  supplied 
under  pressure  from  ordinary  service  mains  to  the  lower  sido  of 
the  piston,  through  the  valve,  JE2,  while  at  the  same  time  the 
opening  of  the  valve,  El,  offers  a  free  passage  for  the  escape  of 
the  water  from  the  upper  and  opposite  side  of  the  piston,  P,  to 
the  atmosphere.  The  result  of  this  unbalanced  pressure  on  the 


FIG.  251. 


316       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

piston  is  to  raise  it,  together  with  the  contact  plates,  $  and  T, 
attached  to  the  piston  rod,  so  that  the  pointer  of  I  is  free  to 
deflect  further  toward  the  left.  As  long  as  the  torque  of 
J,  exerted  by  the  current  flowing  through  the  mechanism,  is 
less  than  the  restraining  force  offered  by  the  springs,  I  will 
remain  in  contact  with  S,  but  as  S  moves  up  a  position  will 


FIG.  252. 

finally  be  attained  where  the  forces  acting  on  the  needle  are  in 
equilibrium,  and  its  extremity  will  therefore  rest  between  the 
plates  S  and  T,  but  not  in  contact  with  either. 

If  an  increasing  load  were  applied  to  /,  the  pair  of  valves,  F1 
and  _F2,  would  be  opened,  and  T  and  S  would  rise  instead  of 
fall.  A  pointer,  R,  is  attached  to  the  piston  rod  and  moves 
over  a  scale  which  is  divided  so  that  the  values  of  the  current 
strengths  may  be  read  off  directly.  The  same  rod  carries  also 


RECORDING  INSTRUMENTS. 


317 


an  inking  pen  that  rests  in  contact  with  the  clockwork-driven 
record  sheet. 

A  detail  view  of  one  of  the  electrically  operated  valves  is  shown 
in  Fig.  253,  which  is  practically  self-explanatory.  The  upper  part 
of  this  apparatus  is  held  to  the  lower  one  by  means  of  a  clamp, 
so  that  if  it  is  desired  to  have  access  to  the  valve  at  any  time 
this  can  be  done  by  the  simple  removal  of  a  screw.  A  copper 
diaphragm  is  interposed  between  the  windings  of  the  electro- 
magnet and  the  iron  core  on  which  it  acts,  in  order  that  moisture 
may  not  enter  and  spoil  the  windings. 

The  possibility  of 
varying  the  outline  of 
the  gap  left  between 
the  plates  S  and  T  of 
the  recorder  forms  an 
interesting  feature  of 
this  apparatus.  If  the 
instrument  whose  fluc- 
tuations are  to  be  re-  \ 
corded  is  of  the  equally  { 
divided  scale  type  in 
which  equal  current 
increments  give  equal 
increase  of  angular 
displacement  of  the 
needle,  the  straight 
slot  illustrated  is  em- 
ployed, and  the  result- 
ant record  chart  is  one 
for  which  ordinary  cross-section  paper  may  be  employed,  like 
numbers  of  divisions  of  the  ordinates  indicating  like  amounts 
of  current  at  all  points  between  the  horizontal  reference  line 
and  the  boundary  full  capacity  line.  This  enables  the  mean 
height  of  the  record  curve  to  be  determined  by  simple  integra- 
tion of  its  inclosed  area  with  a  planimeter  and  dividing  this  by 
the  length  of  the  chart,  as  in  the  case  of  steam  engine  indicator 
cards. 

If  the  excursions  of  the  pointer  of  the  indicating  instrument 
do  not  vary  in  direct  proportion  to  the  changes  in  current 
strength  and  the  straight  gap  is  used,  the  chart  divisions  would 


FIG.  253. 


318       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


be  like  the  scale  divisions,  i.e.9  if  the  latter  are  crowded  together 
at  any  part  of  the  scale  the  chart  abscissae  will  be  close  together 
at  the  same  part.  By  suitably  curving  the  slot,  however,  it  is  pos- 
sible to  make  an  indicating  instrument  movement  whose  scale 
divisions  are  not  of  equal  width  give  a  chart  with  equal  divi- 
sions by  causing  the  excursions  of  the  piston  to  vary  in  direct 
proportion  to  the  current  strength.  With  an  alternating-cur- 
rent voltmeter  having  a  scale  of  the  character  shown  in  Fig.  149 
the  slot  required  to  enable  the  use  of  ordinary  section  paper  as 
a  chart  would  be  shaped  somewhat  like  that  shown  in  Fig.  254. 
It  will  be  seen  that  when  the  contact  on  the  needle  is  at 
the  point  A  a  very  slight  swing  of  the  needle  is  sufficient  to 
close  the  circuit  in  one  direction  or  another,  that  if  the  needle 
is  near  the  point  B  it  will  make  a  larger  angular  swing  before 
coming  in  contact  with  a  plate,  and  that  when  it  is  at  £  the 
original  status  of  affairs  recurs,  except  that  here  the  contact 
may  move  a  little  further,  as  the  scale  of 
the  indicating  instrument  is  more  open 
at  the  highest  point  of  its  range  than  at 
its  lowest. 

CONTACT    TROUBLES. 

In  all  of  the  relay  recorders  so  far  de- 
scribed, the  mechanism  of  an  ordinary 
indicating  voltmeter,  ammeter,  watt- 
meter, or  galvanometer  is  obliged  to  ex- 
ert a  sufficient  torque  to  cause  a  metallic 
button  carried  by  its  needle  to  make  an  electrical  contact  with 
a  stop. 

Even  with  fresh,  smooth  surfaces  the  pressure  that  must  be 
exerted  to  force  them  together  firmly  enough  to  obtain  good 
electrical  contact  is  appreciable,  and  as  the  contacts  become 
somewhat  roughened,  due  to  the  slight  but  constant  sparking 
when  the  motor  or  clutch  circuit  is  made  and  broken  thereat, 
the  pressure  required  becomes  still  higher. 

The  requirement  of  high  contact  pressure  means  low  sensibil- 
ity of  the  instrument  as  a  whole,  and  its  failure  to  record  small 
fluctuations,  as  large  current  changes  must  take  place  before 
the  contact  carried  by  the  movable  element  is  pressed  against  its 
mate  with  the  requisite  force.  Obviously  a  very  small  particle 


FlG.  254. 


RECORDING  INSTRUMENTS. 


319 


of  dust  lodging  between  the  contacts  will  have  the  same 
effect. 

This  difficulty,  while  seemingly  trivial,  has  proven  to  be  the 
greatest  drawback  to  relay  instruments,  and  in  fact  is  the  principal 
reason  why  none  of  them  are  yet  in  extensive  use  although 
their  inception  dates  back  many  years. 

Various  devices  have  been  employed  to  minimize  the  trouble, 
the  more  prominent  being  the  following : 

Rubbing   Contacts. 

Fig.  255  shows  the  expedient  devised  by  Professor  Callendar 
for  use  in  his  recorder.  As  will  be  seen  from  this,  the  needle,  S, 


Threcul&ett 


FIG.  255. 


of  the  galvanometer  plays  between  two  contacts  which  are  made 
in  the  form  of  wheels  that  are  being  slowly  rotated  by  a  light 
thread  belt  driven  by  a  clockwork  mechanism.  Each  wheel  is 
of  brass,  and  into  its  periphery  there  is  let  a  circle  of  platinum 
wire  which  projects  above  the  wheel  face.  The  tip  of  the 
galvanometer  needle  is  of  platinum  also,  so  that  when  it  defects 
against  either  wheel  edge,  a  contact  is  made  between  platinum 
and  platinum,  and  one  of  the  faces  is  kept  rotating  at  right 
angles  to  the  other,  thereby  not  only  continuously  presenting  a 
fresh  surface,  so  that  the  heat  developed  at  the  point  of  contact 


320      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

is  less  apt  to  prevent  incipient  fusing,  but  the  rubbing  polishes 
the  surfaces  and  thus  tends  to  keep  them  in  good  condition. 

In  the  figure  the  contacts  between  the  wheels  and  the  brake 
circuits  are  shown  as  being  made  through  springs  pressing  on 
the  wheel  hubs.  This  is  often  modified  by  supporting  the  axles 
on  which  the  wheels  turn  in  plain  metallic  bearings,  the  amount 
of  current  to  be  transmitted  being  sufficiently  small  to  admit  of 
this  practice. 

Relays. 

Another  method  of  overcoming  the  difficulty  due  to  handling 
comparatively  large  currents  through  the  contact  made  between 
the  instrument  needle  and  its  stop  is  to  use  ordinary  electric 
relays  similar  to  those  employed  in  telegraph  practice,  so  that 
this  circuit  need  carry  only  enough  current  to  energize  the  relay, 
leaving  the  relay  contacts  to  carry  the  heavy  current  that  is 
necessary  to  work  the  clutches  or  the  motor.  By  this  expe- 
dient the  current  controlled  by  the  instruments  may  be  limited 
to  one  in  which  the  sparking  between  the  needle  contact  and  its 
stops  is  inappreciable,  or  at  all  events  not  enough  to  roughen 
them  with  a  consequent  decrease  in  sensibility. 

Such  relays  are,  however,  open  to  the  objection  that  they 
involve  the  use  of  an  additional  battery  circuit,  and  so  add  con- 
siderably to  the  complexity  of  the  device  and  to  the  fact  that 
they  are  expensive.  Without  them,  on  the  other  hand,  it  is 
exceedingly  difficult,  if  not  impossible,  to  make  a  recorder  of  the 
third  class  that  will  be  free  from  contact  troubles  when  used  for 
extended  periods. 

WADDELL   AND    LEGRAND    RECORDER. 

These  interesting  instruments  are  based  on  a  novel  prin- 
ciple. Referring  to  Fig.  256  herewith,  air  under  a  pressure  of 
approximately  three  pounds  to  the  square  inch  is  supplied 
through  a  pipe,  A,  to  the  instrument.  This  air  is  first  obliged  to 
pass  through  a  long  fine-bore  passage,  B,  and  then  into  a  chamber, 
(7,  of  relatively  large  volume.  This  chamber  is  supplied  with 
an  escape  valve,  7),  which  is  similar  to  a  safety  valve,  the  load 
on  whose  disk,  E,  is  determined  by  the  strength  of  the  current 
to  be  measured.  As  in  the  case  of  any  vessel  provided  with  a 
safety  valve  of  comparatively  very  large  capacity,  the  pressure 


RECORDING  INSTRUMENTS. 


321 


in  the  vessel  is  determined  solely  by  the  blowing-off  pressure  to 
which  the  valve  is  loaded.  Small  variations  in  the  pressure  of 
the  air  supplied  through  A  do  not  vitiate  this  result,  as  the  effec- 
tive area  of  the  passage,  B,  is  so  much  less  than  that  through  the 
valve,  D,  that  the  latter  can  take  care  of  any  of  the  fluctuations 
in  the  rate  of  supply  to  the  chamber,  O.  The  manner  in  which 
the  valve  disk,  E,  is  loaded  by  varying  currents  is  also  shown  in 
the  figure.  A  coil,  F,  of  insulated  wire  is  arranged  in  the  annu- 
lar field  supplied  by  the  magnet,  SN,  with  its  extension  pole 
piece,  s.s.  This  coil  is  supported  on  one  end  of  a  lever,  6r,  that 
is  free  to  oscillate  about  the  fulcrum,  H,  and  is  partially  counter- 
balanced by  the  adjustable  weight,  /.  When  current  flows 
through  the  spool  the  reaction  between  the  magnetic  field  that 


Pen, 


FIG.  256. 

it  furnishes  and  that  of  the  permanent  magnet  exerts  a  pressure 
on  the  valve  that  is  in  direct  proportion  to  the  current  strength. 
The  valve  is  therefore  loaded  in  proportion  to  the  current 
strength,  and  the  pressure  in  the  chamber,  (7,  hence  varies  with 
the  current.  The  recording  device  is  formed  by  a  float,  <7,  that  is 
carried  up  and  down  in  the  manometer,  K,  *by  the  variation  in 
pressure  on  its  surface.  A  pen  is  carried  on  a  rod  that  is  rig- 
idly secured  to  the  float,  and  as  it  is  moved  up  and  down  by  the 
latter  traces  a  line  on  the  chart  that  is  revolved  before  it  by 
clockwork  and  shows  the  variations  in  current  strength. 

A  complete  instrument  of  this  class  is  illustrated  in  Fig.  257. 

As  described,  the  apparatus  is  suitable  only  for  the  measure- 
ment of  continuous  currents,  as  only  these  will  give  the  neces- 


322      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


sary  reaction  between  the  permanent  magnet  and  the  coil 
through  which  the  current  flows.  Alternating  currents  are 
measured  by  substituting  for  the  magnet  and  coil  mechanism, 
any  of  the  indicating  instrument  mechanisms  that  have  been 
described  on  preceding  pages  and  arranging  them  so  that  there 
is  no  restraining  force,  the  needle  instead  pressing  on  the  valve. 
A  modification  of  this  kind  is  the  recorder  for  measuring 


FIG.  257. 

the  total  output  of  a  multiphase  circuit,  this  being  shown 
in  Fig.  258.  Here  the  lever  which  loads  the  valve  is  double 
ended  and  carries  at  each  extremity  a  spool  through  which 
there  flows  current  of  a  strength  proportional  to  the  volt- 
age. Each  spool  works  in  the  field  furnished  by  a  solenoid 
through  which  passes  the  total  current  to  be  measured,  and  each 
end  of  the  lever  is  hence  a  wattmeter.  By  making  the  electrical 
connections  such  that  the  right-hand  end,  A,  of  the  spool  is 


RECORDING  INSTRUMENTS. 


323 


depressed  and  the  left-hand  end,  B,  raised  when  current  flows 
through  its  windings,  the  load  on  the  valve  evidently  is  the 
sum  of  the  efforts.  As  was  pointed  out  on  page  230  the 
output  of  a  three-phase  circuit  is  obtained  by  adding  together  the 
indications  of  two  wattmeters  having  their  series  coils  connected 
in  two  of  the  three  legs  and  the  potential  coils  attached 
respectively  between  each  of  these  legs  and  the  third  one. 
In  the  instrument  in  question,  the  addition  instead  of  being  made 
arithmetically  is  made  mechanically,  in  that  it  is  the  sum  of  the 
efforts  of  the  coils  which  causes  the  downward  pressure  on  the 
valve.  The  same  instrument  or  simple  modification  thereof  can 


of  course  be  used  for  recording  the  output  of  two-phase  or  any 
other  multiphase  lines. 

In  the  actual  apparatus  the  contracted  passage,  B,  Fig.  256,  is 
formed,  not  of  a  long  small  diameter  tube,  but  of  a  series  of 
disks  of  filter  paper  which  are  the  equivalent  of  the  capillary 
tube  pneumatically,  and  which  have  the  incidental  advantage  of 
removing  particles  of  dust  from  the  air  supplied  through  A  in 
the  same  figure,  and  so  preventing  clogging  the  valve,  D.  The 
air  for  working  these  recorders  is  supplied  either  by  a  small  air 
compressor  driven  by  any  suitable  means,  or  through  a  reducing 
valve  from  any  high-pressure  air  supply  that  may  be  available. 


CHAPTER  II. 

INTEGRATING  METERS. 

As  has  already  been  stated,  integrating  meters  are  devices  for 
registering  the  product  of  the  mean  value  of  current  or  power 
supplied  through  a  given  circuit  during  any  given  period,  by 
that  period.  In  the  great  majority  of  cases  they  are  used  to 
measure  the  amount  of  current  or  energy  supplied  to  the  cus- 
tomer of  electricity  in  order  to  form  a  just  and  definite  basis  for 
the  bills.  The  name,  "  recording  meters,"  by  which  they  have 
long  been  known,  is  rapidly  falling  into  disfavor,  and  the*  terms 
"  integrating  meter "  and  "  electricity  meter,"  both  of  which 
describe  them  more  correctly,  are  coming  into  use. 

Because  of  the  fact  that  these  devices  form  the  basis  on 
which  the  charges  are  made  by  central  stations  to  their  custom- 
ers, the  number  in  use  is  exceedingly  large,  and  while  already 
many  times  as  great  as  the  number  of  indicating  or  true  record- 
ing instruments  employed,  is  increasing  at  a  rate  that  is  daily 
becoming  larger.  As  they  are  subject  to  conditions  under 
which  few  of  the  instruments  heretofore  described  are  employed, 
and  as  they  are  inherently  of  such  construction  that  the  wear  is 
greater  and  the  length  of  time  that  they  will  remain  in  calibration 
and  also  their  life  is  shorter,  they  come  under  a  somewhat  differ- 
ent category,  and  their  peculiarities  and  ills  are  more  appropri- 
ately treated  in  a  volume  devoted  to  them  exclusively.  A  brief 
description  of  the  principles  on  which  the  more  prominent  types 
are  based  is,  however,  thought  properly  to  form  a  part  of  a  treat- 
ise on  the  general  subject  of  electric  measurements  and  measur- 
ing apparatus. 

Integrating  meters  may  conveniently  be  divided  into  the 
following  general  classes :  Chemical  meters,  these  being  ones 
in  which  the  desired  current  data  is  obtained  through  electro 
deposition;  motor  meters,  in  which  the  device  showing  the 
current  or  energy  integral  is  actuated  by  an  electric  motor 
mechanism ;  and  mechanical  meters  in  which  a  mechanical 

324 


INTEGRATING  METERS.  325 

integrating  device  like  a  planimeter  is  actuated  by  an  indicating 
instrument  and  its  indications  used  to  show  the  result. 

In  all  of  these  it  is  desired  to  obtain  a  record  of  the  total 
amount  of  energy  passed  through  the  meter,  and  where  the 
apparatus  is  an  integrating  wattmeter,  this  result  is  attained 
directly.  Some  of  the  instruments  give,  however,  not  watt 
hours,  but  ampere  hours,  and  the  resultant  charge  made  to  the 
customer  is  based  011  the  assumption  that  current  has  been 
delivered  at  a  constant  potential.  This  state  of  affairs,  while 
never  actually  existing,  as  the  potential  at  the  customer's  prem- 
ises may  easily  vary  5  per  cent,  is  generally  sufficiently  close 
as  an  average  to  form  a  basis  of  charge  that  is  as  equitable  as  is 
the  watt-hour  basis. 

CHEMICAL   METERS. 
Edison    Chemical  Meters. 

The  most  prominent  and  practically  the  only  representative 
of  the  chemical  meters  is  the  Edison  meter.  It  consists  of  a 
voltameter  in  which  the  plates  are  of  zinc  and  the  solution  of 
zinc-sulphate,  instead  of  copper  and  copper  sulphate,  respec- 
tively, as  in  the  case  of  the  voltameters,  mentioned  on  page  14. 
A  shunt  is  inserted  in  the  supply  circuit  and  combined  with  the 
meter  itself,  so  that  only  a  known  fraction  of  the  total  current 
passes  through  the  voltameter.  Two  voltameter  cells  con- 
nected in  series  with  each  other  are  usually  employed  in  order 
to  afford  a  double  check,  and  a  thermostat  is  also  added  which 
consists  of  a  compound  metallic  strip  that  closes  a  circuit 
through  an  incandescent  lamp  when  the  temperature  falls  too 
low,  so  that  the  heat  from  the  latter  may  serve  to  keep  the 
cells  from  freezing  or  becoming  sufficiently  cold  to  introduce 
errors. 

An  Edison  chemical  meter  is  shown  in  Pig.  259. 

Instruments  of  this  type  possess  the  very  great  advantage  of 
containing  no  moving  parts  and  hence  not  being  subject  to  de- 
terioration. Their  accuracy  is  also  of  the  highest,  as  the  fVt 
that  there  is  no  friction  means  that  the  smallest  loads  are  regis- 
tered with  the  same  accuracy  as  the  greatest  ones  within  their 
capacity.  Further,  there  is  no  inertia,  so  that  if  the  current 
passed  through  them  is  fluctuating  in  strength,  the  meter 


326        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

takes  account  of  it  all  without  having  that  inertia  introduce 
errors  because  of  its  refusal  to  allow  the  apparatus  to  get  up  to 
speed  before  the  current  has  again  fallen.  Its  drawbacks  are 
that  in  order  to  obtain  readings  the  jars  containing  the  plates 
must  be  removed  from  the  meter  and  carried  to  some  point 
where  the  delicate  operations  of  cleaning  and  drying  the  plates 
and  weighing  the  change  in  weight  can  be  attended  to.  Where 
the  instrument  is  in  constant  use,  this  means  that  two  sets  of 
voltameters  must  be  supplied,  the  one  being  in  the  recorder 
while  the  other  is  at  the  station.  An  incidental,  but  impor- 
tant, further  drawback  is  that  the  customer  to  whom  current 


FlG.  259. 

is  being  sold  and  whose  bills  are  figured  from  the  indications 
of  the  recorder,  is  left  without  even  the  crudest  means  for 
ascertaining  what  the  meter  readings  are,  and  is  therefore 
obliged  to  rely  entirely  on  the  accuracy  of  the  station  reports 
as  rendered  in  the  form  of  bills.  The  comic-paper  man 
with  his  gas-meter  jokes  has  rendered  sucli  apparatus  out  of 
the  question.  Even  an  instrument  which  a  customer  can 
read  himself  is  viewed  with  suspicion,  and  when  no  means 
of  this  kind  are  afforded  it  is  generally  a  waste  of  time  and 
breath  to  attempt  to  persuade  him  that  bills  are  not  made 
up  simply  by  guesswork  and  with  an  idea  of  having  them  as 
large  as  he  will  stand  without  protest.  It  is  for  the  latter 


INTEGRATING  METERS. 


327 


reason  in  many  cases,  as  much  as  any  other,  that  the  Edison 
meters  are  going  out  of  use  and  being  replaced  by  integrating 
instruments  of  the  motor  type. 


MOTOR    METERS. 


Thomson  Integrating  Meters. 

One  of  the  oldest  and  certainly  the  most  widely  used  motor 
meter  is  the  Thomson  integrating  watt-hour  instrument  shown 
with  its  protective  casing  removed  in  Fig.  260.  It  consists  of 


FIG.  260. 


an  electric  motor  with  a  vertical  shaft,  the  armature  being  of  the 
drum-wound  type  and  both  it  and  the  field  windings  being  with- 
out iron  cores.  The  armature  wires  are  of  small  diameter  and 
carry  a  current  varying  in  proportion  to  the  potential  between 


328        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

the  service  mains,  acting  like  the  potential  windings  of  an  indi- 
cating wattmeter.  The  field  windings  are  of  heavy  wire,  and 
through  them  is  passed  the  total  current.  The  torque  exerted 
under  these  conditions  is  evidently  proportional  to  the  product 
of  the  simultaneous  instantaneous  values  of  the  current  and 
potential,  that  is  to  say,  to  the  watts,  whether  the  current  is 
direct  or  alternating.  The  load  for  the  motor  is  supplied  by  a 
copper  disk  secured  on  the  lower  part  of  the  shaft  and  rotating 
between  the  pole  faces  of  a  pair  of  permanent  magnets,  the  eddy 
currents  generated  in  the  disk  by  its  rotation  in  this  magnetic 
field  forming  a  drag  that  increases  in  strength  in  direct  propor- 
tion to  the  speed.  As  the  torque  of  the  motor  increases  in 
direct  proportion  to  the  watts,  it  is  clear  that  each  wattage  calls 
forth  a  corresponding  opposing  load  and  that  the  speed  there- 
fore increases  in  direct  proportion  to  the  watts.  It  is  hence 
possible  simply  to  attach  a  train  of  gears  to  be  driver!  by  the 
rotating  shaft  and  to  affix  pointers  to  appropriate  members  of 
this  train  which  will  thereupon  show  on  appropriately  divided 
dials  over  which  they  sweep,  the  watt  hours  that  have  been 
consumed. 

If  the  apparatus  were  frictionless,  it  would  operate  correctly 
when  made  along  the  simple  lines  described.  This  is,  however, 
not  the  case,  as  the  friction  between  the  bearing  on  which  the 
foot  of  the  shaft  rests,  and  between  the  commutator  and  the 
brushes,  is  not  an  inappreciable  quantity.  It  is,  however,  a  quan- 
tity that  may  safely  be  assumed  to  be  nearly  constant  irrespec- 
tive of  the  speed  of  rotation  of  the  shaft,  and  provision  is  hence 
made  to  supply  a  constant  torque  which  will  just  balance  this 
frictional  resistance.  The  means  is  a  coil  wound  like  the  station- 
ary field  coils,  and  of  a  size  that  will  just  slip  inside  of  one  of 
them,  the  coil  being  of  fine  wire  and  connected  in  series  with 
the  armature  and  the  non-inductive  calibrating  resistance.  As 
the  circuit  so  formed  is  always  connected  across  the  mains, 
current  is  continuously  flowing  through  it,  and  by  properly 
adjusting  the  distance  between  the  fixed  coil  and  the  armature, 
the  field  that  the  coil  supplies  may  be  made  of  a  strength  that 
is  just  sufficient  to  make  the  torque  of  the  armature  in  it  one 
that  balances  the  frictional  drag.  In  practice  it  is  necessary  to 
adjust  the  position  of  this  so-called  "  starting  coil "  after  the 
meter  has  been  erected  in  place.  This  is  because  a  meter 


INTEGRATING  METERS. 


329 


subject  to  mechanical  vibration  has  less  friction  of  the  lower 
bearing  than  if  the  same  instrument  were  installed  at  a  perfectly 
quiet  point.  The  adjustment  is  made  empirically,  the  starting 
coil  being  pushed  inward  toward  the  armature  until  the  latter 
just  begins  to  rotate  with  no  current  flowing  through  the  series 
winding,  whereupon  the  coil  is  slightly  retracted  and  then  made 
fast. 

As  there  are  two  series  field  coils  the  instrument  is  easily 
arranged  for  measuring  the  input  on  a  three-wire  circuit,  one  of 
the  coils  being  placed  in  series  with  each  of  the  outer  mains 
and  the  potential  coil  between  one  of  the  outer  mains  and  the 
neutral,  as  is  shown  in  Fig.  261. 

For  very  heavy  currents  such  as  in  central  stations,  the 
current  windings  take  the  form  of  a  flat  copper  bar  as  shown  in 
Fig.  262,  and  two  armatures,  each  of  which  is  placed  within  the 
influence  of  the  field  surrounding  the  bar,  are  used  connected  to 


FIG.  261. 


a  common  shaft.  In  all  of  the  instruments  the  calibration  may 
be  adjusted  by  varying  the  radial  distance  between  the  shaft 
turned  by  the  armature  and  the  center  of  the  pole  faces  embrac- 
ing the  copper  disk  and  so  changing  the  opposing  torque. 


330       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

Sangamo    Integrating   Meters. 

In  this  apparatus,  as  in  the  Thomson  described  above,  a 
motor  exerting  a  torque  proportional  to  the  watt  consumption 
of  the  circuit  in  which  it  is  connected,  rotates  a  disk  of  conduct- 
ing material  between  the  jaws  of  stationary  permanent  magnets, 
and  the  number  of  its  revolutions  as  shown  by  pointers  sweeping 
over  appropriately  divided  dials  is  a  measure  of  the  watt  hours. 


FIG.  262. 

The  motor  element  and  many  of  the  details  of  the  apparatus 
differ  markedly  from  the  Thomson  device.  The  former  will  be 
understood  by  reference  to  accompanying  Fig.  263.  Here  a 
disk,  A,  of  copper  provided  with  a  float  chamber,'^,  is  sub- 
merged in  a  bath  of  mercury,  (7,  inclosed  in  a  chamber  of 
insulating  material,  D.  Bedded  into  the  walls  of  the  chamber 
are  a  block  of  iron,  6r6r',  and  the  extremities,  EE',  of  a 
laminated  core  electromagnet  EFEf.  Copper  lugs,  HH',  are 


INTEGRATING  METERS. 


331 


also  bedded  into  the  chamber  at  diametrically  opposite  points. 
When  such  a  structure  is  connected  in  circuit  as  the  figure 
shows,  the  disk,  J.,  is  evidently  located  within  the  field  of  force 
of  the  electromagnet,  the  flux  direction  being  from  E  to  6r 
and  from  6r'  to  Jtf *  The  disk  at  the  same  time  is  being 
traversed  by  a  current  flowing  in  the  direction  shown  by  the 
arrows,  coming  in  through  the  lug,  H,  through  the  short  gap 
between  A  and  H  that  is  filled  with  mercury,  and  similarly  out 
from  A  to  Hf .  We  thus  have  an  Arago  disk  motor  whose 
torque  is  in  proportion  to  the  watt  consumption  of  the  load 
under  measurement,  as  the  disk  current  is  that  required  by  the 


FIG.  %J(£. 


load,  while  the  magnetic  field  against  which  it  reacts  is  of  a 
strength  proportional  to  the  applied  potential,  the  windings  of 
the  electromagnet  being  connected  across  the  supply  line. 

In  this  meter  the  device  for  obtaining  a  small  and  adjustable 
initial  torque  to  compensate  for  the  retardational  effect  of  the 
friction  of  the  moving  parts  consists  of  a  small  spiral  of  bare 
resistance  wire  wound  on  a  hard  rubber  rod  and  electrically 
connected  at  J  and  K  in  shunt  to  the  disk  circuit.  Current 
for  the  potential  circuit  of  the  meter  is  tapped  off  from  this 
spiral  at  any  desired  point  of  its  length  by  shifting  along  the 
movable  contact,  L.  The  resistance  of  the  spiral  is  high  as 


332      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

compared  with  that  of  the  circuit  through  the  disk.  With  L 
near  J,  the  major  portion  of  the  current  drawn  by  the  windings, 
JV,  of  the  potential  circuit,  evidently  flows  direct  from  J  through 
LN  to  M-,  a  small  portion  only  flowing  through  the  by-path, 
JHAH'KL,  owing  to  the  much  higher  resistance  of  that  path. 
There  is  then  but  a  feeble  current  through  the  disk,  A.  When 
L  is  moved  over  to  K,  the  high  resistance  of  the  spiral  means 
that  the  major  portion  of  the  potential  circuit  current  flows 
through  the  disk  circuit  instead  of  through  JK  as  before,  and 
similarly  for  intermediate  positions  of  L.  The  proportions 
are  such  that  this  small  current  which  constantly  flows 
through  the  disk,  independent  of  the  load,  may,  by  shifting 
X,  be  brought  to  a  value  setting  up  a  torque  which  just 
balances  friction. 

The  meters  are  claimed  to  be  superior  to  the  Thomson  form. 
For  one  thing  the  commutator,  which  is  always  a  more  or  less 
troublesome  element  and  a  source  of  variable  friction  errors,  is 
eliminated.  For  another  thing,  the  buoyant  effect  of  the 
mercury  is  utilized  to  entirely  relieve  the  lower  shaft  bearing 
of  the  weight  of  the  moving  system ;  in  fact,  the  design  gives  a 

very  slight  upward  thrust  of 
about  two  per  cent  of  down- 
ward pressure  in  a  non-floated 
meter.  This  reduced  press- 
ure means  greatly  decreased 
friction  and  wear  and  a  much 
lessened  liability  to  injury  of 
the  jewel  or  staff  end  if  the 
apparatus  is  jarred  or  run  sub- 
ject to  vibration.  Another 
feature  is  the  ability  to  use 
shunts  similar  to  those  util- 
ized with  indicating  ammeters 
of  the  direct-current  type,  to 
increase  the  ampere  capacity. 
This  point  is  of  a  decided  ad- 
vantage from  the  standpoint 
FIG.  264.  of  cost,  as  a  shunt  can  be 

built  for  a  fraction  of  the  expense  involved  in  constructing  the 
stationary  conductors  in  a  commutator  type  meter  of  material 


INTEGRATING  METERS. 


333 


heavy  enough  to  carry  currents  of  high  value.     Shunts  are  not 
feasible  with  commutator  apparatus. 

Fig.  264  shows  the  parts  of  the  motor  member  of  a 
Sangarno  meter  disassembled  and  arranged  one  above  the  other 
in  the  order  in  which  they  go  together.  The  downwardly  pro- 
jecting tube  on  the  top  cover  plate  contains  a  pierced  jewel 
through  which  the  shaft,  P,  Fig.  263,  passes  and  which  acts  as 
a  guide  bearing  for  that  shaft.  The  fact  that  the  minute  clear- 
ance between  the  shaft  and  its  bearing  is  the  only  point  where 
mercury  could  escape,  and 
that  the  mercury  can  never 
get  at  that  point  owing  to 
the  "  patent  ink  well "  type 
of  construction,  makes  it  pos- 
sible to  ship  such  apparatus 
from  place  to  place  with  the 
mercury  in  position  and 
without  danger  of  spilling 
any  of  it. 

A  Sangamo  meter  with 
the  cover  removed  is  shown 
in  Fig.  265. 

Aaron  Meter. 

The  Aaron  integrating  in- 
strument can  be  considered 
as  belonging  to  the  class  of 
motor  meters  only  in  that 
the  indices  which  show  the 
current  or  energy  consumption  are  driven  over  the  dials  by 
spring  motors.  The  apparatus  is  not  in  use  in  this  country, 
and  it  is  doubtful  whether  it  ever  will  be  employed  to  any 
extent  here,  as  it  is  both  bulky  and  costly  and  rather  too 
complex  to  suit  the  fancy  of  our  engineers.  Its  ingenious  prin- 
ciple, however,  entitles  it  to  at  least  brief  mention  in  this 
volume. 

The  apparatus  takes  on  many  different  forms,  according  to 
the  kind  of  circuit  on  which  it  is  to  be  used,  but  all  rest 
on  the  following  principle :  Two  separate  clockworks  having 
escapements  of  the  pendulum  pattern  are  mounted  together 


FlG.  265. 


334       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


on  a  common  framework,  and  these  are  adjusted  so  that  their 
rate  is  exactly  the  same.  The  two  trains  of  clockwork  mesh 
into  two  gears,  P  and  P'  respectively  (Fig.  266),  which  gears, 
together  with  the  pinion,  J,  form  a  device  like  the  gear  in  the 
Callendar  recorder  illustrated  in  Fig.  247.  As  long  as  the 
trains  are  moving  at  the  same  rate,  P  and  P'  will  rotate 
without  causing  the  shaft  that  carries  I  to  rotate  about  its 
axis,  X.  If,  however,  one  of  the  trains  should  be  caused  to 
run  more  slowly  than  the  other,  X  will  be  rotated,  and  the 
pinion  on  it  will  set  the  indicating  hands  attached  to  the  gears 
in  mesh  with  the  pinion  which  it  carries  in  rotation  over  their 

respective  dials. 

A  difference  in  speed 
of  the  gear  trains  of  the 
two  clocks  is  brought 
about  and  made  to  vary 
in  proportion  to  the 
strength  of  the  measured 
current  in  the  following 
way:  Referring  to  Fig. 
267,  which  shows  an 
Aaron  meter  with  the 
case  open,  it  can  be  seen 
that  the  lefkhand  one  of 
the  clocks  is  provided 
with  an  ordinary  pendulum,  this  being  made  of  brass  or  any  other 
non-magnetic  material.  The  bob  of  the  right-hand  pendulum 
is  a  U-shaped  permanent  magnet,  which  swings  over  the  end  of 
a  solenoid  through  which  the  current  to  be  measured  is  passed. 
When  no  current  is  flowing  the  solenoid  of  course  exerts  no 
influence  on  the  magnet,  and  the  clocks  are  free  to  run  at  the 
like  speed  to  which  they  are  primarily  adjusted.  When,  how- 
ever, current  flows,  the  swings  of  the  magnet  are  retarded,  and 
the  amount  of  retardation  increases  in  direct  proportion  to  the 
current  strength. 

For  alternating-current  work,  a  laminated  iron  core  swinging 
within  a  horizontally  placed  solenoid  is  substituted  for  the 
other  arrangement,  and  for  the  measurement  of  watt  hours 
instead  of  ampere  hours  the  pendulum  bob  is  formed  of  a 
coil  of  fine  wire  that  is  connected  across  the  line  through 


FIG.  266. 


INTEGRATING  METERS. 


335 


the  interposition  of  a  suitable  auxiliary  resistance.  As  the 
planes  of  the  fixed  and  swinging  coils  are  parallel,  the  attraction 
between  them  varies  with  the  watts,  as  in  the  case  of  an  indicate 
ing  wattmeter.  Other  possible  modifications  rendering  the 
apparatus  suitable  for  use  on  three-wire  and  multiphase  circuits 
will  suggest  themselves. 

ALTERNATING-CURRENT   METERS. 

The  Thomson  commutator  meter  above  described  and  others 
of  its  class  may  be  used  011  alternating  as  well  as  direct 
current,  just  as  a  dyna- 
mometer type  wattmeter 
is  available  for  either  kind 
of  circuit,  but  they  are 
but  seldom  so  employed 
in  practice,  principally  be- 
cause  the  commutator 
with  its  attendant  ills  and 
the  heavy  duty  on  the 
jewel  bearing  because  of 
the  great  weight  of  the 
moving  system,  are  con- 
sidered evils  to  be  tol- 
erated only  where  their 
presence  is  essential.  The 
Sangamo  meter  in  which, 
as  explained,  the  commu- 
tator is  absent  and  the 
jewel  pressure  extremely 
small,  forms  an  acceptable 
alternating-current  device 
when  a  condenser  is  in- 
serted in  the  potential 
circuit  to  compensate  for 
the  self-induction  of  that  winding  and  cause  the  changes  in 
magnetization  of  the  iron  core  to  vary  in  phase  with  the  line 
potential.  This  pattern  is  relatively  new,  but  seems  growing 
in  favor. 

The  class  of  meter  for  alternating-current  service   in   most 
extensive   use  is,  however,   the  induction    type,  which,  while 


FIG.  267. 


336      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

operative  only  on  alternating  circuits,  is  attractive  because  of 
its  simplicity  and  durability. 

The  earliest  form  of  induction  meter  that  came  into  general 
service  is  the 

Shallenberger  Meter. 

The  Shallenberger  meter  records  ampere  hours  and,  as  is  seen 
from  Fig.  268,  contains  a  stationary  flattened  coil  of  heavy  wire 
through  which  the  current  to  be  measured  is  passed.  Within 
this  coil  there  is  a  second  one  similarly  shaped,  and  placed  with 
its  longitudinal  axis  at  an  angle  to  the  above  series  coil  and 
having  its  windings  short-circuited  on  itself.  Located  in  the 
plane  of  both  coils  is  an  aluminum  disk.  The  alternating  cur- 
rent flowing  through  the  outer  coil  produces  another  current  in 
the  short-circuited  one,  and  the  resultant  of  the  magnetic  fields 
set  up  by  the  two  is  evidently  shifting  around  the  axis  £>f  the 

inclosed  disk.  This  rotating 
field  carries  the  disk  along 
with  it,  the  torque  being  di- 
rectly proportional  to  the 
current  in  the  series  coil. 
The  torque  opposing  the  ro- 
tation of  the  aluminum  disk 
is  furnished  by  four  light 
vanes  of  aluminum  secured 
to  radial  arms,  forming  a  fan 
whose  opposing  torque  varies 
as  the  speed  and  the  work 

necessary  to  rotate  it,  as  the  square  of  the  speed.  The  revolu- 
tions of  the  rotating  element  are  registered  by  a  train  of  gears 
driven  by  the  rotating  shaft  as  in  other  motor  meters. 

Induction  Wattmeters. 

The  Shallenberger  meter  above  mentioned  is  evidently  an 
ampere-hour  meter.  Induction  instruments  may  be  built  to 
register  watt  hours  instead  by  causing  a  rotatably  mounted 
disk  or  drum  of  good  conducting  material,  usually  aluminum,  to 
be  acted  upon  by  two  sets  of  coils,  one  carrying  the  line  current 
and  the  other  a  current  varying  in  proportion  to  the  applied 
potential  and  hence  connected  across  the  line.  In  order  that 
these  two  currents  may  set  up  a  rotating  magnetic  field  so  as  to 


INTEGRATING  METERS.  337 

cany  the  aluminum  disk  along  and  thus  drive  the  train  of  gears 
actuating  the  indices  which  show  the  watt  hours  consumption, 
one  must  be  displaced  in  phase  from  the  other.  This  is  accom- 
plished in  commercial  meters  by  placing  in  series  with  the 
potential  winding,  which  is  connected  across  the  line,  a  highly 
inductive  resistance  which  of  course  causes  the  phase  of  the 
current  flowing  therethrough  to  be  displaced  nearly  ninety 
degrees.  The  torque  exerted  on  the  rotatable  member  is  pro- 
portional to  the  product  of  the  simultaneous  instantaneous 
strengths  of  the  currents  in  the  two  windings,  that  is  to  say, 
to  the  watts  being  expended  in  the  circuit  beyond. 

The  mechanical  disposition  of  the  elements  of  such  meters 
evidently  admits  of  considerable  variation. 

MECHANICALLY    INTEGRATING   METERS. 

A  type  of  integrating  meter  possessing  many  attractive  fea- 
tures and  which  is  periodically  re-invented,  consists  in  transfer- 
ring the  indications  of  an  indicating  ammeter  or  wattmeter  to  a 
clockwork  or  motor-driven  counting  train.  The  needle  of  the 
indicating  instrument  swings  over  a  scale  as  usual  and  carries  a 
stop  or  else  some  transmitting  device.  A  clockwork  operated 
mechanism  is  set  in  motion  at  successive  intervals  of  time,  and 
either  rotates  through  a  distance  determined  by  the  position  of 
the  stop  as  determined  by  tho  load  passing  through  the  instru- 
ment, or  works  the  counting  train  through  a  transfer  gear  car- 
ried by  the  needle  for  a  length  of  time  that  is  likewise  determined 
by  the  needle's  position. 

The  number  of  such  devices  in  actual  use  is  so  exceedingly 
small  that  the  devotion  of  any  extended  space  to  them  and  their 
peculiarities  and  drawbacks  is  not  warranted.  Mention  is  made 
as  the  principle  at  least  is  of  interest. 

BOYLE    INTEGRATOR. 

Another  form  of  integrating  meter  in  which  the  mechanism 
of  an  indicating  device  is  utilized  is  the  recorder  mentioned  on 
page  314.  To  the  rod  which  carries  the  record  pen  and  the 
index  that  sweeps  over  the  graduated  scale,  there  is  secured,  as 
is  seen  from  Fig.  269,  an  arm  with  a  fork-shaped  end  which  in 
rising  carries  with  it  a  small  wheel,  A.  A  is  free  to  slide  along 
the  ?haft,  B,  which  has  at  its  end  a  worm  that  drives  the  count- 


338     ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


ing  train.  A  drives  B  in  that  the  latter  is  provided  with  a 
key-way  running  for  its  whole  length,  A  being  supplied  with  a 
feather  that  runs  in  it.  A  is  in  contact  with  the  face  of  a  large 
disk,  D,  that  is  driven  by  clockwork  at  a  constant  speed,  and 
the  plane  of  whose  face  is  at  right  angles  to  that  of  A.  When 
A  is  at  the  center  of  D  the  latter  will  rotate  without  causing  A 


FIG.  269. 

to  turn ;  when,  however,  A  is  carried  above  the  center  by  the 
fork  J7,  D  will  drive  it  and  hence  the  counting  train,  and  the 
rate  of  rotation  will  be  in  direct  proportion  to  the  distance  of 
.F  from  the  center.  The  latter  distance  is  proportional  to  the 
current  through  the  meter  which  controls  the  position  of  the 
needle,  U,  on  the  scale,  S,  and  the  counting  train  hence  gives  am- 
pere or  watt  hours  according  as  that  meter  is  an  ampere  or  a 
wattmeter. 


CHAPTER   III. 


MAXIMUM    DEMAND    METERS. 

IN  order  to  be  able  to  charge  the  purchaser  of  electrical 
energy  an  equitable  amount,  it  is  desirable  to  know  not  only  the 
product  of  the  mean  value  of  the  energy  by  time  it  was  supplied, 
but  also  to  know  the  maximum  amount  that  has  been  called  for 
during  any  appreciable  period,  in  order  that  the  purchaser  may 
be  properly  taxed  for  that  proper- 
tion  of  the  total  supply  equip- 
ment  that  must  be  held  in  reserve 
for  him,  so  that  he  may  make  that 
demand  at  any  time.  Instruments 
for  measuring  this  largest  call  are 
known  as  maximum  demand,  or 
simply  demand,  meters. 

Wright  Maximum  Meters. 

This  instrument,  which  is  illus- 
trated in  Fig.  270,  consists  of  a 
U-shaped  glass  tube,  having  en- 
larged chambers  at  both  extremi- 
ties and  a  side  tube  opening  out 
of  one  of  them.  The  chamber 
that  has  not  the  side  outlet  is  sur- 
rounded with  a  couple  of  turns  of 
high-resistance  alloy  that  is  made 
in  the  form  of  a  thin  ribbon  wound 
tightly  about  the  chamber,  in  order 
that  the  heat  generated  therein 
by  the  passage  of  the  current  may  waism  the  air  in  the  chamber. 
The  tube  is  filled  with  liquid  to  about  the  height  shown. 
When  current  flows  through  the  resistance  strip  the  expansion 
of  the  air  in  the  chamber,  A,  due  to  the  heat,  forces  the 
surface  of  the  liquid  in  the  left-hand  leg  of  the  tube  down- 
ward, and  that  in  the  right-hand  one  correspondingly  up 


FIG.  270. 


340      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

ward.  Should  the  current  strength  be  sufficiently  high,  the 
surface  of  R  will  rise  until  the  liquid  will  overflow  into  the 
central  tube,  8.  If  the  current  is  then  reduced  or  cut  off,  and 
afterward  put  on  again,  R  cannot  rise  sufficiently  to  overflow 
into  S  unless  the  current  strength  is  greater  than  the  preceding 
one.  The  greater  the  current,  however,  the  greater  is  the 

amount  of  liquid  that  will  flow  into 
the  center  tube,  and  the  scale  placed 
alongside  of  the  tube  may,  therefore, 
be  graduated  to  show  the  maximum 
amperage  that  has  passed  through 
the  heater  strip.  The  air  in  the 
chamber,  A,  does  not  heat  up  in- 
stantaneously, and  the  surface  of  R, 
therefore,  does  not  vary  at  once  with 
change  in  current  strength,  but  lags 
considerably  behind  it,  the  time  ele- 
ment being  such  that  if  a  given  cur- 
rent flows  through  the  winding  for 
five  minutes,  only  about  80  per  cent 
of  the  amount  of  liquid  will  flow  into 
8  that  would  get  there  if  the  cur- 
rent were  left  on  indefinitely :  about 
95  per  cent  of  the  total  amount  will 
be  measured  in  ten  minutes,  and  all 
of  it  in  half  an  hour.  This  feature 
is  of  importance,  as  it  means  that 
the  customer  is  not  penalized  because 
of  the  existence  of  a  momentary 
short  circuit  on  his  line,  which  does 
not  injure  the  supply  station  in  any 
way,  and  account  is  not  taken  of  a 
heavy  current  momentarily  drawn, 
as  when  starting-  a  motor,  which  also 

FIG.  271.  ,  ' 

does  not  inconvenience  the  station. 

The  meter  can  be  reset,  that  is,  the  liquid  drained  out  of  the 
tube,  S,  by  inverting  the  U-shaped  portion  so  that  it  all  flows 
into  the  chamber,  B,  as  after  it  is  lowered  to  its  original  position 
again  that  liquid  will  flow  into  R  instead  of  8.  Variations  in 
the  temperature  of  the  atmosphere  do  not  affect  the  device,  as 


MAXIMUM   DEMAND  METERS. 


341 


it  is  in  reality  simply  a  maximum  indicating  differential  ther- 
mometer actuated  by  the  difference  in  temperature  between  its 
two  bulbs.  The  apparatus  is  put  in  a  locked  case,  so  that  this 
resetting  cannot  be  done  Iby  unauthorized  parties.  A  complete 
instrument  is  shown  in  Fig.  271. 

Schattner  Maximum  Mater. 

In  this  device,  illustrated  in  Fig.  272,  a  glass  tube  bent  as 
shown  is  partially  filled  with  steel  balls  which  fit  its  bore  quite 
closely,  and  then  entirely  filled  with  an  oil  of  greater  or  less 


FIG.  272. 

viscosity,  according  to  the  lag  in  indications  desired,  after  which 
it  is  sealed.  This  tube  is  then  secured  by  clips  to  the  sector- 
shaped  plate  carried  by  a  suitably  journaled  shaft,  which  shaft 
is  rotated  over  an  angle  proportionate  to  the  strength  of  the  cur- 
rent flowing  through  the  curved  solenoid  in  the  lower  left-hand 
corner  of  the  containing  case  because  of  the  attraction  cf  that 
solenoid  on  its  iron  core.  As  the  sector  and  hence  the  tube  are 
so  tilted,  the  steel  balls,  which  are  initially  all  contained  in  the 
tube's  curved  arm,  tend  to  run  out  of  this  arm  and  down  into  the 
straight  one.  The  curvature  is  such  that  for  a  small  inclination 


342       ELECTRIC   AND  MAGNETIC  MEASUREMENTS. 

only  one  ball  is  on  a  downward  grade  and  that  the  number  so 
situated  increases  with  the  angular  deflection  of  the  sector. 
The  oil  in  the  tube  gives  a  dashpot  effect  to  the  movement  of 
the  steel  balls  such  that  a  momentary  overload  or  short  circuit 
would  not  be  registered,  that  is  to  say  it  introduces  the  same 
time  lag  that  exists  in  the  indications  of  the  Wright  meter. 
Different  lags  are  obtained  by  using  oils  of  different  viscosities. 

On  the  face  of  the  sector  is  printed  a  table  as  shown,  giving 
the  ampere  flows  through  the  solenoid  required  to  cause  varying 
numbers  of  balls  to  run  down  into  the  straight  tube.  The 
sector  also  has  marked  on  it  just  above  the  curved  tube,  a  scale 
graduated  in  amperes,  the  position  of  said  scale  relative  to  a 
stationary  pointer  carried  by  the  containing  case,  thus  giving 
a  means  of  reading  the  instantaneous  values  of  the  current 
strength. 

This  meter  is  reset,  that  is,  the  balls  returned  to  their  initial 
positions  in  the  curved  arm  after  taking  a  reading  by  removing 
the  tube  from  its  clips  and  hanging  it  upside  down.  As  this 
operation  is  rather  a  slow  one,  a  spare  tube  is  often  supplied 
fastened  in  an  inverted  position  inside  of  the  case,  and  this  is 
exchanged  for  the  first  one  as  readings  are  made. 


PART   III. 


CHAPTER    I. 
MAGNETIC  UNITS. 

THE  elementary  magnet  is  a  straight  thin  rod  or  bar  whose 
manifestations  of  maximum  magnetic  energy  are  exerted  at  or, 
near  its  ends  at  points  known  as  the  magnet  poles.  All  magnets 
have  two  poles,  which  are  termed  by  convention  positive  and 
negative,  the  former  being  that  which  points  toward  the  north 
if  the  magnet  is  freely  suspended  in  the  earth's  magnetic  field. 
Magnetic  poles  of  like  sign  mutually  repel  one  another  and 
poles  of  unlike  sign  attract  one  another  with  forces  that  in  both 
cases  are  directly  proportional  to  the  product  of  the  strengths 
of  the  two  poles  and  inversely  proportional  to  the  square  of  the 
distance  between  them. 

UNIT    MAGNETIC   POLE. 

The  unit  magnetic  pole  is  taken  as  one  which  will  act  on  a 
pole  of  like  strength  with  a  unit  of  force  (1  dyne)  when  placed 
at  a  unit  distance  (1  cm.)  therefrom. 

POLE    STRENGTH. 

The  paths  in  the  space  surrounding  a  magnet,  throughout 
which  magnetic  actions  of  equal  force  exist,  form  closed  curves 
starting  from  one  pole  and  extending  through  the  surrounding 
medium  back  to  the  other.  They  are  the  lines  seen  when 
iron  filings  are  sprinkled  on  a  piece  of  glass  or  paper  under 
which  a  magnet  is  placed,  as  in  the  familiar  illustrations  found 
in  every  textbook  of  physics.  When  it  is  desired  to  ascertain 
their  direction  it  is  done  by  this  sprinkling  method,  or,  when 
that  is  not  feasible,  by  suspending  a  very  short  and  very  thin 
magnetized  needle  so  that  it  is  free  to  assume  any  position  and 
plotting  its  successive  directions  when  moved  about  in  the  field 
to  be  explored.  Such  a  needle  is  shown  in  Fig.  273. 

Although  the  number  of  paths  is  infinite  for  every  magnet, 

343 


344      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

by  convention  lines  of  force  are  utilized  to  designate  the 
strength  of  the  magnetic  field  as  well  as  to  show  its  direction, 
one  line  of  force  per  unit  of  area  (1  square  crn.) 
at  right  angles  to  its  direction  being  taken  as 
representing  the  unit  force.  This  unit  force  is 
that  exerted  by  a  unit  pole  at  a  distance  of  1  cm. 
As  the  surface  surrounding  the  ideal  unit  pole  is 
a  sphere  and  has  an  area  of  4?rr,  and  as  r  is 
unity  at  the  unit  distance,  the  number  of  lines 
of  magnetic  force  that  proceed  from  a  unit  pole 
is  4?r,  which  is  thus  the  unit  pole  strength ; 
its  symbol  is  usually  written  m. 

STRENGTH    OF   FIELD. 

The  strength  or  intensity  of  a  magnetic  field  at  any  point  is 
measured  by  the  force  that  it  would  exert  on  a  unit  magnetic 
pole  placed  at  that  point,  and  therefore  under  the  above  con- 
vention is  the  number  of  lines  of  force  per  square  cm.  there. 
Field  strength  is  designated  by  the  symbol  If. 

MAGNETIZING    FORCE. 

Usually  the  force  causing  a  magnetic  flux  through  a  given 
circuit  is  supplied  by  a  coil  or  solenoid  of  wire  through  which 
an  electric  current  is  being  passed.  If  that  solenoid  has  a 
length  which  is  great  as  compared  with  its  diameter,  the  direc- 
tions of  the  lines  of  force  within  it  will  be  parallel  except  at 
the  ends.  If  the  coil  has  JV  turns,  its  length  is  L,  and  the  cur- 
rent through  it  is  expressed  in  absolute  units  (1  absolute  unit 
equals  10  amperes)  the  magnetizing  force  of  the  solenoid  exerted 

on  the  medium  within  it  is  5  for  if  a  unit  pole  were  moved 

10Z/ 

along  one  of  the  lines  of  force  within  the  solenoid  for  a  distance 
of  1  cm.  its  4?r  lines  would  cut  JV-s-  L  turns  of  wire,  generating 

an  E.M.F.  of  — — -  and  the  work  done  would  be  -  -=-• 
-L  \\j_L 

This  is  the  strength  of  the  field  within  the  coil,  and  is,  there- 
fore, also  the  H  above.  The  number  of  turns  per  unit  of  length 

N 

of  the  solenoid  is  often  written  ^,  that  is,  -=-  =  n ;  in  this  case 

Ju 

the  above  formula  becomes   - 


MAGNETIC   UNITS.  345 

MAGNETIC   INDUCTION. 

If  the  core  of  the  above  solenoid  were  of  a  magnetic  material, 
say  iron,  instead  of  air,  while  the  magnetizing  force  H  would 
remain  the  same,  the  flux  of  magnetic  force  through  the  core 
would  become  very  much  greater.  The  value  of  this  induced 
flux  is  dependent  not  only  on  the  nature  of  the  material  forming 
the  core,  that  is  to  say,  whether  it  is  of  iron,  steel,  cobalt,  etc., 
but  on  the  magnitude  of  the  magnetizing  force,  i.e.,  on  the  value 
of  H.  Flux  density  is  designated  by  the  symbol  B,  and  its 
unit,  the  Gauss,  is  one  line  of  force  per  square  cm.  of  cross- 
section. 

PERMEABILITY. 

The  ratio  of  the  magnetizing  force  to  the  magnetic  induction, 
that  is,  of  B  to  H,  is  the  magnetic  permeability,  and  is  usually 
written  /A.  If  the  core  within  the  solenoid  is  made  a  vacuum, 
H  equals  B  and  /JL  equals  1. 

The  permeability  of  all  gases,  liquids,  and  solids,  with  the 
exception  of  nickel,  cobalt,  and  iron  and  its  compounds,  is  at 
ordinary  temperatures  practically  that  of  the  vacuum  that  is 
used  as  the  unit.  No  known  substance  has  a  permeability  of 
zero  ;  that  is,  there  is  no  known  substance  that  will  prevent  the 
flow  of  a  magnetic  flux,  and  none  has  a  sufficiently  low  value 
of  fji  to  be  considered  as  a  magnetic  insulator  in  the  sense  that 
glass,  rubber,  etc.,  are  electrical  insulators. 

MAGNETOMOTIVE   FORCE. 

The  magnetizing  force  that  drives  a  flux  through  a  reluctance 
is  called  a  magnetomotive  force.  As  the  magnetizing  force 
If  is  simply  the  magnetomotive  force  per  unit  of  length  of  the 
magnetizing  coil,  the  value  of  the  magnetomotive  force  of  a 

•1    -       TT     T  TT  47TJV7  4:7TNI  ,, 

given  coil  is  H,  L,  or  as  H  =  is    —  ^  —       Magnetomo- 


tive  force  is  expressed  in  gilberts,   and,  as  is  seen  from  the 
formula,  a  gilbert  is  .7958  ampere  turns.     Its  symbol  is  F. 


MAGNETIC    MOMENT. 


If  a  straight-bar  magnet  is  freely  suspended  in  a  uniform 
magnetic  field  it  will  take  up  a  position  such  that  its  axis  is 
parallel  to  the  lines  of  force.  The  turning  moment  tending  to 


346      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

bring  it  into  parallelism  is  a  maximum  when  the  bar  is  at  right 
angles  to  the  field  and  is  dependent  on  the  distance  between  the 
magnet  poles,  the  strength  of  the  poles,  and  the  strength  of  the 
field.  If  H,  the  field  strength,  is  unity,  the  moment,  M,  of 
the  magnet  is  the  product  of  the  strength  of  either  pole  by  the 
distance  between  them,  that  is  to  say,  it  is  ml. 

INTENSITY    OF    MAGNETIZATION. 

The  intensity  of  magnetization,  J,  of  a  magnet  having  its  poles 
at  its  ends  is  the  pole  strength,  m,  divided  by  the  polar  area  & 
It  is  also  the  magnetic  moment,  My  of  the  magnet  divided  by  its 

Y 

volume,    V,  for  if  I  is  the  length,  V  =  IS,    or  S  =   — .     The 

M 

moment  is    M—  Im,  or  m  =  —     Substituting  these  values  in 

'  A 

the  formula  for  pole  strength,  we  have  —  = — 

8  V 

The  relations  in  a  magnetic  circuit  are  governed  by  the  law : 
flux  equals  magnetomotive  force  divided  by  reluctance,  a  form- 
ula that  is  easily  recognized  as  being  analogous  to  Ohm's  law 
for  electric  circuits. 


CHAPTER  II. 

MEASUREMENT  OF  FIELD  STRENGTH. 
BY    CALCULATION. 

THE  strength  of  the  magnetic  field  within  a  solenoid  having 
a  non-magnetic  core  may  be  calculated  directly  from  the  form- 

ula H  =  -  —  =  —  given  on  page  344.     The  number  of  turns,  -ZV, 
3  0  /> 

is  counted,  the  length  of  the  solenoid,  X,  is  measured,  and  the 
current,  J,  read  with  the  aid  of  any  appropriate  currenkmeasur- 
ing  instrument. 

Where  the  field  to  be  measured  is  that  of  a  permanent  mag- 
net, or  where  for  other  reasons  the  method  of  calculation  can- 
not be  employed,  means  of  direct  measurement  must  be  resorted 
to.  The  first  of  these  is  the 

METHOD    OF    OSCILLATION    OF    A    MAGNET. 

This  is  due  to  Gauss  and  is  suitable  only  for  the  measure- 
ment of  very  weak  fields,  as,  for  instance,  that  of  the  earth. 
Two  sets  of  observations  must  be  made,  the  first  being  the  time 
of  oscillation  of  a  suspended  magnet,  and  the  second  the  deflec- 
tions of  that  magnet  when  acted  on  by  the  field  of  another. 
The  first  gives  the  value  of  the  product,  MH,  from  the  formula 

Tf  2 

=  MR.      In  this  formula  K  is  the  moment  of  inertia  of 


the  magnet,  t  the  time  of  a  single  oscillation  of  the  magnet,  and  6 
the  ratio  of  torsion  of  the  supporting  thread.  If  the  magnet 
is  a  simple  geometrical  body  and  known  to  be  homogeneous, 
its  moment  of  inertia  can  be  calculated  from  its  weight  and 
dimensions  in  the  ordinary  way.  If  it  is  irregular  the  following 
expedient  may  be  adopted.  The  time  of  a  single  oscillation,  with 
the  magnet  in  its  original  condition,  is  first  observed  and  re- 
corded. It  is  then  loaded  with  a  ring  whose  mass  and  dimen- 
sions are  known,  and  whose  own  time  of  inertia  can  therefore 
be  calculated.  The  magnet  loaded  with  this  ring  is  then  set 

347 


348       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 
swinging  and  the  time  of  an  oscillation  noted  as    before.     If 


this  time  be  called  ^  the  value  of  MJT=—  --  ^——  -2  -  -^  .  The 

(l  +  0)  (r  --  tx  ) 

ratio  of  torsion  in  the  formula  is  the  ratio  between  the  restoring 
forces  due  to  the  elasticity  of  the  suspension  and  to  the  action 
of  the  magnetic  fields  respectively  when  the  magnet  is  only 
slightly  deflected  from  the  magnetic  meridian.  To  find  its 
value,  the  torsion  head  attached  to  the  suspension  carrying  the 
magnet  should  be  twisted  through  an  angle  of  about  360 
degrees  and  the  resulting  deflection  noted.  If  the  angle  of  twist 
of  the  torsion  head  is  called  a  and  that  of  the  deflection  5, 

6=  --     The  time  of  oscillation,  £,  is  best  observed  with 

a  —  o 

the  aid  of  a  stop-watch  and  a  telescope  and  scale  or  lamp  and 
scale  arrangement,  such  as  that  used  with  reflecting  gal^anom- 
eters  (see  page  42). 

The  second  observation  in  the  oscillation  method  of  measure- 
ment of  weak  fields  is  that  of  the  ratio  of  M  to  H.  To  obtain 
it,  it  is  necessary  to  use  a  magnetometer,  a  device  for  comparing 
the  magnetic  moments  of  different  magnets.  The  magnetometer 
consists  of  a  light  silvered  mirror,  to  the  back  of  which  are 
cemented  two  or  three  short  strips  of  magnetized  watch  spring 
which  serve  as  a  small  magnetic  needle.  This  will  of  course 
hang  with  its  plane  in  the  magnetic  meridian.  The  magnet, 
whose  time  of  oscillation  has  been  determined,  is  now  placed 
with  its  axis  at  right  angles  to  the  axis  of  the  magnetometer 
needle  and  will  thereupon  cause  the  magnetometer  reading  to 
change.  The  angular  deflection  of  the  magnetometer  is  noted, 
as  is  also  the  distance  between  the  center  of  the  test  bar  and 
the  instrument.  Call  the  distance  between  the  center  of  the 
magnetometer  needle  and  the  magnet  r.  The  operation  is  then 
to  be  repeated,  using  a  different  value  for  the  distance  between 
the  magnetometer  needle  and  the  bar.  Call  this  distance  ^  and 
let  the  corresponding  angular  deflections  be  </>  and  (pl.  The 

value  _  .,  is  then 

M  _  r5  tan  <f>  —  r  f  tan  <£* 


In  testing  any  weak  field  extreme  care  must  be  taken  to  see 
that  there  are  no  bodies  of  magnetic  material  in  the  immediate 


MEASUREMENT  OF  FIELD  STRENGTH.      349 

vicinity  of  the  apparatus,  and  that  there  are  no  movable  mag- 
netic masses,  even  if  they  are  nothing  but  a  bunch  of  keys  car- 
ried in  the  pocket,  as  either  will  seriously  modify  the  field  and 
introduce  large  errors  in  the  results.  The  conditions  are  par- 
ticularly difficult  when  measuring  the  intensity  of  the  earth's 
field,  as  this  is  always  varying  slightly  in  itself  and  is  much 
influenced  by  the  fields  due  to  current-carrying  conductors,, 

INDUCTION    METHODS.        (SNAP   AND    ROTATING    COILS.) 

If  a  conductor  consisting  of  N  turns  of  wire  and  inclosing  an 
area,  S,  is  placed  in  a  magnetic  field  of  uniform  intensity,  J?,  it 
is  traversed  by  a  total  flux,  SH,  if  its  plane  is  at  right  angles 
to  the  direction  of  the  lines  of  force.  If  this  coil  is  sharply 
rotated  through  180  degrees  about  a  diametral  axis,  an  E.M.F. 
will  be  induced  therein  having  a  value  of  2  N/SIL  This  E.M.F. 
lasts  but  momentarily,  and  a  ballistic  galvanometer  must  be 
utilized  if  it  is  to  be  observed.  Suppose  such  a  galvanometer 
to  be  attached  to  the  terminals  of  such  a  coil,  and  that  galva- 
nometer resistance  is  g.  Let  the  resistance  of  the  coil  be  r  and 
that  of  the  leads  plus  any  auxiliary  resistances  that  may  be 
placed  in  the  circuit  in  order  to  bring  the  galvanometer  deflec- 
tion down  to  a  reasonable  point  be  R.  The  E.M.F.  generated  by 
the  rotation  of  the  coil  would  then  cause  the  quantity  of  electric- 

2NSH 

ity  q  =—        —  p  to  flow  through  the  galvanometer  circuit.     The 

value  of  _/Z~can  be  calculated  directly  from  this  formula  if  the 
galvanometer  constant  is  known.  The  latter  can  be  found  for 
any  particular  instrument  by  discharging  a  condenser  through 
it,  in  the  usual  manner. 

If  the  gap  in  which  the  field  to  be  measured  exists  is  so 
narrow  that  it  is  impossible  to  rotate  the  coil  of  wire,  it  can  be 
sharply  moved  by  hand  at  right  angles  to  the  lines  of  force  or 
the  same  thing  accomplished  with  a  trigger-released,  spring- 
actuated  device.  In  this  modification  the  formula  becomes 

JTa  7  7VT 

,  in  which  I  is  the  distance  through  which  th°  coil 


has  been  moved. 

This  latter  method  must  be  used  in  the  narrow  clearance  space 
existing  between  the  armature  and  the  pole  pieces  of  a  dynamo 
or  motor,  and  the  coil  is  usually  moved,  not  between  two  fixed 


350        ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

limits,  but  between  a  position  in  the  gap  and  one  outside  of  it 
where  the  field  does  not  exist,  as  this  is  easier  than  attempting 
to  arrest  a  coil  suddenly  and  accurately. 

The  rotation  method  is  more  convenient  when  there  is  sufficient 
space  to  allow  of  revolving  the  coils,  and  is  specially  useful  in 
measuring  the  intensity  of  the  stray  field  of  generators.  If  the 
angle  of  rotation  is  made  exactly  180  degrees,  the  results 
obtained  are  very  reliable. 

The  rotating  coil  method  may  also  be  used  for  the  determina- 
tion of  weak  fields  such  as  that  of  the  earth  if  the  coil  area  S  is 
made  very  large. 

BISMUTH    SPIRAL. 

The  metal  bismuth  has  the  peculiar  property  of  offering  an 
increased  electrical  resistance  when  placed  in  a  magnetic  field. 
The  intensity  of  the  field  can  be  measured  from  this  increase  in 


FIG.  274. 

resistance,  being  proportional  to  the  difference  between  the  re- 
sistance when  in  the  field  and  when  out  of  it  divided  by  the  re- 
sistance when  out  of  it.  The  actual  apparatus  for  measuring 
field  strength  in  this  way  takes  the  form  of  a  flat  spiral  of 
bismuth  wire  doubled  back  on  itself,  so  as  to  avoid  induction 
errors,  and  attached  to  a  handle  as  shown  in  Fig.  274.  The 
windings  are  held  in  place  by  being  cemented  between  two 
plates  of  mica  and  form  a  coil  so  thin  that  it  can  easily  be  intro- 
duced into  the  clearance  space  between  an  armature  and  its 
field  magnets.  The  resistance  of  the  coil  when  not  within  the 


MEASUREMENT  OF  FIELD  STRENGTH. 


351 


influence  of  a  field  is  usually  made  about  10  ohms.  The  relation 
between  the  field  strength  and  resistance  is  determined  separately 
for  each  spiral  and  remains  sensibly  constant  under  all  commer- 
cial circumstances.  The  varying  resistance  is  easily  determined 
with  the  aid  of  a  bridge,  and  the  field  strength  found  by  consult- 
ing a  table  or  curve  which  comes  with  the  coil,  or  in  some 
instances,  by  having  the  bridge  specially  calibrated,  so  that  when 
used  with  a  given  spiral  the  values  of  H  are  indicated  directly. 
Fig.  275  shows  the  calibration  curve  of  an  average  specimen. 

ELECTROMAGNETIC    METHOD. 

In  the  commercial  ammeters  and  voltmeters  of  the  permanent 
magnet  pattern  described  in  Chapter  VI,  current  strength  is 
measured  by  the  reaction  between  a  constant  field  and  the 


0.7 
0.6 
?Q5 
0.4 
0.3 
0.2 
O.I 
QO 

^ 

x^ 

x*"^ 

^ 

x* 

^x 

^ 

\ 

x^ 

"5? 

£ 

x^ 

x 

x^ 

,-—  - 

^ 

2000          4000       6000          8000         10000       GOOD        <4000       BOO 
F»  Lines  of  Force  per  Sq  Cm 
FIG.  275. 

unknown  current,  as  indicated  by  an  index  attached  to  a  moving 
coil  working  against  a  spring  which  offers  an  opposing  force  like 
the  spring  in  a  spring  balance.  It  is  evident  that  the  reverse  of 
this  method  can  be  used  to  measure  the  strength  of  the  field  if 
the  strength  of  the  current  flowing  through  the  movable  con- 
ductor is  known.  An  apparatus  based  on  this  principle  is  shown 
in  Fig.  276.  Here  a  conductor,  £,  is  rigidly  attached  to  an  arm, 
(7,  a  known  current  measured  by  an  ammeter  being  passed 
through  I  by  means  of  the  flexible  strips//'.  If  I  is  introduced 
into  the  gap  in  a  magnetic  circuit  so  that  the  current  through 
it  flows  at  right  angles  to  the  lines  of  force,  it  will  be  -acted 
upon  by  a  force  IHl  in  which  I  is  the  current,  H  the  field  inten- 
sity, and  I  the  length  of  the  conductor.  The  force  is  measured 
by  varying  the  tension  of  the  spring  R  by  turning  the  screw  V. 


352      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

The  screw  is  calibrated  so  that  the  force  exerted  is  known  and 
a  micrometer  index  attached  to  it  can  therefore  be  made  to  indi- 


.p 


FIG.  276. 

cate  field  strengths  directly  with   the   current  J  adjusted  to  a 

given  value. 

The  shortness  of  the  length,  7,  and  the  small  current  that  may 
be  passed  through  it  because  of  the  neces- 
sity of  making  the  conducting  strips,  //,  so 
thin  that  they  offer  no  appreciable  resist- 
ance to  Z's  movement,  makes  the  forces 
involved  small,  so  that  such  apparatus  can 
be  used  only  for  the  measurement  of  power- 
ful fields. 

Various  modifications  of  this  apparatus 
dependent  on  the  reaction  between  the  field 
and  a  current-carrying  conductor  will  sug- 
gest themselves. 

MIOT   INDUCTIOMETER. 

An  interesting  piece  of  apparatus  for 
measuring  field  strength  is  the  Miot  In- 
ductiometer  illustrated  in  Fig.  277.  It 
consists  of  a  three-legged  glass  tube  filled 
with  mercury  to  the  level  shown  by  the 
heavily  shaded  areas.  A  similarly  shaped 
but  shorter  three-legged  tube  is  attached  to  its  lower  end  by  means 
of  rubber  tubing,  so  that  it  can  be  placed  at  any  desired  angle 
to  the  upper  one.  The  lower  member  of  the  short  tube  is  placed 
in  the  field  whose  strength  is  to  be  measured  and  current  passed 


FIG.  277. 


MEASUREMENT  OF  FIELD  STRENGTH.  353 

through  the  mercury  contained  therein  in  the  direction  indicated 
by  the  arrows.  The  position  of  the  lower  tube  is  made  such 
that  the  flow  of  current  traverses  the  fields  perpendicular  to  the 
lines  of  force,  and  therefore  the  reaction  between  that  field  and 
the  current  through  the  mercury  causes  the  latter  to  rise  in  the 
central  tube.  The  elevation  of  the  mercury  there,  as  indicated 
by  the  rise  in  the  surface  of  the  column  of  liquid  that  is  poured 
over  its  surface,  is  proportional  to  the  field  strength  and  to  the 
current  through  the  mercury,  in  other  words,  ITequals  KhL  K 
is  a  constant  which  is  separately  determined  for  every  inductio- 
meter,  n  is  the  head  of  liquid  as  measured  by  the  scale  placed 
alongside  of  the  central  tube,  and  Jis  read  from  an  ammeter 
placed  in  the  current  circuit.  For  any  given  current  the  scale 
can  evidently  be  divided  so  as  to  show  If  directly. 


CHAPTER   III. 
MEASUREMENT  OF  PERMEABILITY. 

THE  determination  of  the  permeability,  /-t,  of  various  speci- 
mens of  magnetic  material  is  of  the  utmost  importance  in  the 
calculation  of  electrical  machinery,  as  on  this  quality  depends 
the  magnetizing  force  that  must  be  supplied  to  obtain  a  mag- 
netic field  of  sufficient  strength  to  obtain  the  desired  reactions. 

It  is  more  difficult  to  make  this  determination  than  that  of 
electrical  conductivity,  chiefly  because  of  the  fact  that  a  joint 
in  a  magnetic  circuit  such  as  must  be  used  in  the  majority  of 
permeability  measuring  devices  has,  unless  made  with  extreme 
care,  a  magnetic  resistance  that  is  so  high  as  compared  with 
that  of  the  iron  that  errors  amounting  to  over  100  per  cent  are 
only  too  readily  introduced.  Take,  for  instance,  a  case  in  which 
the  air  gap  between  two  of  the  magnetic  conductors  forming 
the  circuit  is  as  small  as  .01  mm. ;  if  /JL  is  2000  this  is  the 
resistance  of  a  four  millimeter  length  of  the  iron  and  means  that 
a  corresponding  error  will  be  present  in  the  result.  It  is  there- 
fore clear  that  with  short  specimens  great  pains  must  be  taken  to 
obtain  a  perfect  magnetic  contact,  machining  the  surfaces  as  true 
as  possible  and  then  tightly  clamping  them  together  by  appro- 
priate devices  such  as  screws,  etc0  Another  difficulty  in  per- 
meability measurements  is  that,  as  already  stated,  there  is  no 
magnetic  insulator,  and  hence  no  way  of  confining  the  flux  to  a 
given  path,  so  that  leakage  factors  of  unknown  magnitude  must 
be  allowed  for. 

As  the  value  of  ft  varies  with  different  values  of  the  magnet- 
izing force,  it  is  necessary,  in  order  to  obtain  a  complete  record 
of  the  behavior  of  a  given  specimen,  to  subject  it  to  fields  of 
varying  intensities.  A  specimen  should  first  of  all  be  entirely 
demagnetized ;  to  accomplish  this,  it  is  surrounded  by  a  magne- 
tizing coil  through  which  an  alternating  current  is  passed  of 
a  value  such  that  the  bar  will  be  magnetized  more  strongly 
than  it  has  been  since  subject  to  the  last  magnetization.  The 
current  should  then  be  gradually  decreased  in  strength  by 

354 


MEASUREMENT  OF  PERMEABILITY.  355 

inserting  an  external  resistance  until  it  is  reduced  to  the  lowest 
possible  value,  whereupon  it  should  be  cut  off.  The  minimum 
value  of  the  demagnetizing  current  should  be  made  very  low 
indeed,  this  being  conveniently  accomplished  by  utilizing  a  liquid 
resistance,  in  which  the  distance  between  two  plates  immersed 
in  an  electrolyte  may  be  constantly  increased  until  one  plate  is 
finally  withdrawn. 

The  bar  is  now  magnetized  by  passing  a  small  current  through 
the  surrounding  solenoid  and  observing  by  one  of  the  methods 
to  be  described  later  on  the  flux  induced  therein. 

The  exciting  current  is  then  increased  by  successive  steps  and 
the  various  values  of  B  corresponding  to  different  ones  of  H 
plotted  in  the  form  of  a  curve.  A  set  of  such  curves  from  soft 
steel,  wrought  iron,  and  cast  iron  specimens  is  shown  in  Fig.  278. 
It  will  be  noted  that  in  each  case  the  value  of  B  increases  with 
an  increase  in  the  value  of  H,  at  first  quite  slowly,  then  more 
rapidly  to  a  maximum  rate,  and  finally  more  slowly  again.  If 
the  curve  were  prolonged  at  the  upper  end  it  would  be  found 
that  a  value  of  H  would  soon  be  reached  at  which  the  curve 
became  a  straight  line,  B  increasing  in  direct  proportion  to  H 
only  and  the  iron  thus  acting  like  an  air  core.  At  this  point 
the  iron  is  said  to  be  "  saturated." 

For  reasons  that  will  be  made  apparent  in  the  chapter  on 
hysteresis,  it  is  necessary  in  all  permeability  tests  to  see  that 
the  strength  of  the  magnetizing  current  is  increased  from  each 
step  to  the  next  and  not  allowed  to  first  fall  and  then  rise  to  the 
new  value. 

MAGNETOMETRIC  METHOD. 

The  permeability  of  a  given  specimen  may  be  determined 
with  the  aid  of  a  magnetometer  as  follows :  — 

The  specimen  should  be  a  rod  having  a  length  at  least  four 
hundred  and  preferably  as  much  as  five  hundred  times  its  diam- 
eter, and  be  enclosed  in  a  magnetizing  coil  which  is  slightly  longer 
than  itself.  The  rod  should  be  placed  vertically  at  a  known 
distance  from  a  magnetometer.  The  solenoid  that  energizes  the 
bar  in  itself  affects  the  magnetometer,  and  this  action  must  be 
compensated  for  by  the  addition  of  coreless  solenoid  placed  with 
its  axis  horizontal  in  a  position  found  by  experiment  where  the 
current  passed  through  it,  and  the  bar  solenoid  in  series  no  longer 
produces  any  effect. 


356       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

It  is  generally  found  that  the  vertical  component  of  the 
earth's  magnetism  acts  on  the  test  specimen  also,  and  this  must 
then  be  compensated  for  by  an  auxiliary  winding  through  which 
a  current  of  appropriate  strength  is  kept  flowing.  A  rheostat 


FIG.  278. 


is  inserted  in  the  circuit  energizing  the  vertical  compensating 
winding,  and  another  in  that  of  the  bar  energizing  solenoid, 
so  that  the  value  of  H  may  be  adjusted  at  will,  the  whole  appa- 
ratus being  connected  as  shown  in  Fig.  279. 


MEASUREMENT  OF  PERMEABILITY. 


357 


After  being  set  up,  the  compensation  for  the  effect  of  the 
main  solenoid  on  the  magnetometer  is  accomplished  by  shifting 
the  coil  as  already  indicated.  The  adjustment  of  the  current 
through  the  solenoid  that  compensates  for  the  vertical  compo- 
nent of  the  earth's  field  is  affected  by  first  causing  the  maximum 
current  to  be  employed  to  flow  through  the  main  winding  and 
then  gradually  decreasing  it  to  zero  by  increasing  the  resistance 
in  the  rheostat  R,  the  current  being  rapidly  reversed  at  the  same 
time  by  means  of  a  suitable  commutator.  If  the  magnetometer 
shows  no  traces  of  magnetism  of  the  bar  when  R  has  reduced 
the  current  value  to  zero, 
the  strength  of  the  current 
through  a  b  is  correct;  if 
action  does  exist,  the 
strength  of  the  current 
through  ah  must  be  adjusted 
until  this  disappears. 

We  now  have  the  equip- 
ment so  arranged  that  the 
strength  of  the  magnet  N  iS 
can  be  measured  by  the  mag- 
netometer, this  being  ob- 
tained in  terms  of  the 
strength  He  of  the  earth's 
field  at  the  point  of  obser- 
vation. The  test  bar  is  so 
long  that  its  poles  maysafely 
be  assumed  as  being  at  the 
extreme  ends,  and  the  dis- 

i  ,,  ,  FIG.  279. 

tance  between  the  poles  is 

so  great  that  the  magnetometer  may  be  considered  as  being  in- 
fluenced by  the  upper  one  only. 

To  obtain  the  curve  showing  the  value  of  //.  the  magnetizing 
current  is  increased  in  the  desired  number  of  steps  and  the 
corresponding  values  of  the  induction  plotted.  The  value  of 

H,  the  magnetizing  force,  is  obtained  from  the  formula  — JQ-» 

which  has  already  been  given. 

Owing  to  the  fact  that  it  is  necessary  to  know  the  value  of 
the  earth's  field  where  the  permeability  test  is  being  made  by 


^*-i^W^eA^4^-*^xAe^c^«^ 


858      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

magnetometric  method  as  well  as  to  the  complication  of  the 
apparatus  involved,  and  the  fact  that  the  test  bar  must  be  of 
dimensions  such  that  it  can  rarely  be  a  piece  selected  from 
material  that  is  to  enter  into  the  construction  of  electrical  appli- 
ances, this  method  is  but  seldom  used  outside  of  a  laboratory. 
Its  chief  value  is  in  the  determination  of  the  permeability  at 
very  low  magnetizing  forces,  as  these  act  sluggishly  and  the 
magnetometer  will  record  the  final  effect,  whereas  in  most  of  the 
other  methods  to  be  described  further  on  such  is  not  the  case. 

BALLISTIC     METHODS. 

In  the  snap  coil  method  of  measuring  field  .strength  the 
E.M.F.  induced  in  the  coil  by  its  movement  through  the  field 
as  indicated  by  a  ballistic  galvanometer  is  used  to  determine  the 
strength  of  the  field.  As  relative  motion  between  the  coil  and 
the  magnetic  flux  is  all  that  is  necessary,  the  same  results  may 
be  had  by  keeping  the  coil  stationary  and  causing  the  flux  cir- 
cuit to  collapse,  so  that  the  lines  of  force  cut  the  coil. 

Straight  Bar  Ballistic  Test. 

If  the  specimen  to  be  measured  can  be  supplied  in  the  form 
of  a  long  thin  rod  of  the  dimensions  mentioned  in  the  preceding 
paragraph,  its  permeability  can  be  determined  with  a  ballistic 
galvanometer  as  follows : 

The  bar-  is  placed  within  a  magnetizing  solenoid  as  before, 
but  wound  around  the  center  of  the  solenoid  there  is  placed  an 
auxiliary  winding  of  several  turns  of  wire  whose  terminals  are 
connected  to  the  ballistic  galvanometer.  If  current  is  suddenly 
sent  through  the  solenoid,  or  if  a  current  already  flowing 
through  it  is  abruptly  interrupted,  an  E.M.P.  will  be  induced  in 
the  test  coil,  which  will  be  shown  by  the  deflection  of  the  ballis- 
tic instrument.  If  if  is  the  galvanometer  constant,  /the  current 
strength,  and  N  the  turns  per  centimeter  length  of  solenoid  the 

4  TrNI       S 
value  of  B  can  be  found  from  the  equation  B  =  K  — ^ —  X  -~ 

in  which  s  is  the  galvanometer  throw  with  the  test  bar  in  place, 
arid  S  the  same  before  the  bar  was  inserted.  Successive  values 
of  fju  are  obtained  by  making  as  many  successive  readings. 

Rowland  Method. 

In  this  the  specimen  to  be  tested  must  be  circular  in  shape 
having  a  small  radial  breadth.  This  ring  is  covered  by  hand 


MEASUREMENT  OF  PERMEABILITY.  359 

with  a  known  number  of  turns  of  wire,  and  the  strength  of  the 
current  flowing  therethrough  may  be  regulated  as  desired  by 
means  of  a  rheostat,  and  measured  by  an  ammeter,  as  shown  in 
Fig.  280.  Over  a  section  of  the  magnetizing  winding  there  is 
wound  a  test  coil  of  several  turns  of  fine  wire  having  its  termi- 
nals connected  to  a  ballistic  galvanometer. 

In  making  the  test  the  ring  must  first  of  all  be  thoroughly 
demagnetized  by  the  method  outlined  above.  Current  is  then 
caused  to  flow  through  the  energizing  winding,  and  when  this  is 
suddenly  made  or  broken  the  change  in  flux  will  produce  cur- 
rents in  the  exploring  coil,  and  these,  as  indicated  by  the  galva- 
nometer, form  a  means  of  obtaining  the  data  sought.  The  value 

,  4*rwJ  -rllO  10*  .       ,  .  ,    _.     . 

of  IT  is     .,  .  _   as  above,  and  of  J5,  K—= in  which  JTis  the 

10  I  2  an 

galvanometer  constant,  R  the  resistance  of  the  test  coil  circuit,  6 


FIG.  2 


the  throw  of  the  galvanometer,  a  the  cross-sectional  area  of  the 
ring,  and  n  the  number  of  turns  in  the  test  coil  From  the 
two  we  have  the  value  of  /z. 

While  it  is  easier  to  make  the  test  specimen  in  the  form  of  a 
ring  than  to  obtain  the  long  straight  bar,  the  inconvenience  of 
placing  the  winding  on  it  by  hand  is  so  great  that  this  test  is 
seldom  resorted  to.  A  modification  which  overcomes  this  dis- 
advantage is  the 

Hopkinson  Divided  Bar  Method. 

Here  the  test  specimen  takes  the  form  of  a  rod  again,  but 
one  of  convenient  dimensions,  usually  about  one  half  inch  diam- 
eter by  14  to  18  inches  length,  cut  into  two  parts.  This  rod  is 
inserted  into  holes  drilled  in  a  very  heavy  wrought-iron  yoke,  as 
illustrated  in  Fig.  281.  The  right-hand  half  of  the  bar  is  solidly 
secured  in  place  by  means  of  a  clamp  screw,  but  the  left-hand 


360       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

one  may  be  pulled  out  by  means  of  the  handle  shown.  The 
exciting  coil  supplying  the  magnetomotive  force  to  drive  the 
flux  through  the  specimen  is  in  two  parts,  wound  on  appropriate 
bobbins,  and  separated  by  a  space  sufficient  to  admit  of  the 
insertion  of  another  and  so-called  test  coil  wound  concentrically 
with  the  exciting  coil.  The  exciting  current  is  taken  from  a  set 
of  batteries,  measured  by  an  ammeter  and  sent  in  one  or  the 
other  direction  through  the  coils  with  the  aid  of  a  reversing 
switch.  The  test  coil  has  its  terminals  attached  to  a  ballistic 
galvanometer,  as  is  shown  in  the  figure.  This  test  coil  fits 
loosely  in  its  place  and  an  elastic  cord  keeps  it  pulled  against 
the  test  bar,  so  that  if  the  movable  section  is  pulled  out  the  test 
coil  will  be  snapped  out  sidewise  clear  of  the  whole  apparatus. 


FIG.  281. 

In  making  the  test  the  exciting  current  is  adjusted  by  the 
rheostat  to  the  desired  value  in  the  regular  way,  the  test  bar 
handle  pulled  so  that  the  test  coil  snaps  out  and  the  resultant 
galvanometer  deflection  is  noted.  As  the  test  coil  cuts  the 
whole  flux  present  when  the  handle  was  pulled  the  galvanometer 
deflection  is  a  measure  of  the  flux.  The  formula  connecting 

T>A 

the    two    is    B  =  K~— 108,  the  significance  of   the  symbols 

being  as  before. 

The  magnetizing  force,  #,  is  calculated  from  the  number  of 
turns  in  the  exciting  coil  and  the  strength  of  the  current  flowing 

through  it  as  usual  ( H  =  —57^7-  )• 
\  1U  I  / 


MEASUREMENT  OF  PERMEABILITY. 


361 


In  this  divided  bar  method,  correction  must  be  made  for  the 
fact  that,  as  the  test  specimen  does  not  fit  closely  within  the 
exciting  coils,  many  lines  of  force  pass  through  the  test  coil  that 
do  not  flow  through  the  specimen.  The  value  of  this  correction 
is  easily  determined  by  making  a  preliminary  measurement,  using 
a  non-magnetic  test  bar  in  place  of  the  regular  specimen. 

The  Hopkinson  method  assumes  that  the  magnetic  resistance 
of  the  yoke  is  so  small  that  the  length  of  the  magnetic  circuit 
is  the  length  of  the  bar  between  the  yoke  faces.  It  also  assumes 
that  the  magnetic  resistance  between  the  test  bar  and  the  yoke 
is  negligible. 

Neither  assumption  is  rigorously  correct  and  the  method  can 
hence  be  used  only  when  approximate  determinations  are  all 
that  are  required. 

The  Drysdale  Permeameter. 

A  great  objection  to  most  of  the  devices  for  the  measurement 
of  permeability  is  that  it  is  necessary  to  prepare  special  test 
specimens.  Where  these  are  made  from  lots  of  sheet  metal  such 
as  is  used  in  the  construction  of  transformers  and  armatures,  the 
specimen  can  as  a  rule  be  safely  taken  as  a  fair  representative 
of  the  character  of  the  lot.  When,  however,  the  test  is  to  be 
made  on  cast  metal,  either  iron  or  steel,  such  as  enters  into  the 
construction  of  dynamos  and  motors,  a  test  bar  cast  from  the 
same  pouring  as  the  frame  itself  cools  so  much  more  quickly 
than  the  rest  that  the  physical  character  of  the  metal  is  changed, 
and  this  affects  the  magnetic  qualities  very  seriously.  To  cut  a 
piece  out  of  the  casting  is  both  expensive  and  unreliable,  as  if  a 
fin-like  projection  is  left  to  be  machined 

rapidly   as 


off  it   will   cool    much   more 
would  a  separate  test  bar. 

A  device  to  overcome  these  objections 
has  recently  (see  "  Proceedings  of  the 
American  Institute  of  Electrical  Engi- 
neers," November,  1901)  been  devised  by 
Drysdale.  A  special  drill  is  used  with 
which  a  hole  is  drilled  in  the  mass  of  the 
material  to  be  tested,  leaving  a  cylindrical  central  core,  as 
shown  by  the  cross-sectional  illustration  given  in  Fig.  282.  A 
tapered  iron  plug  carrying  at  its  lower  extremity  a  pair  of  coils 


FIG.  282. 


362      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


of  insulated  wire  is  arranged  to  fit  in  this  hole  and  when  pushed 
in  place,  as  shown  by  Fig.  283,  forms  a  magnetic  circuit  in  which 
the  central  core  left  is  energized  by  one  of  the  coils,  the  other 

coil  being  for  connection 
to  a  ballistic  galvanometer, 
as  in  the  case  of  all  tests  of 
this  kind.  The  return  mag- 
netic circuit  is  through  the 
surrounding  body  of  the 
mass  of  metal  under  test, 
and  through  the  testing 
plug. 

Connections  are  made,  as 
in  Fig.  284,  and  the  various 
galvanometer  throws  corre- 
sponding to  the  reversals  in 
the  exciting  current  with 
different  values  of  that  cur- 
rent are  plotted  in  the  regu- 
lar way. 

In  order  to  have  a  com- 
plete self-contained  commercial  apparatus,  the  batteries,  the 
rheostat  for  varying  the  strength  of  the  exciting  current,  the 
reversing  switch,  the  ammeter  for  measuring  current  strength, 
and  the  ballistic  galvanometer  are  all  built  into  one  case,  as 
shown  in  Fig.  285,  a  compartment  being  added  to  receive  the 
test  plug  and  the  cords  making  connection  with  same.  The 


FIG.  283. 


FlG.  284. 


ammeter,  JL,  is  calibrated  in  amperes,  and  the  ballistic  galvano- 
meter, B,  is  made  with  a  needle  swinging  over  a  scale  instead  of 
a  light  spot  and  is  calibrated  directly  in  gausses. 

It  is  advisable  to  make  the  test  at  three  or  four  different  points 


MEASUREMENT  OF  PERMEABILITY. 


363 


in  the  mass  ol  metal  under  examination,  to  be  sure  that  no  error 
has  been  introduced  because  of  drilling  into  an  unexpected  flaw. 

When  necessary  to  restore  the  original  condition  of  the  mag- 
netic circuit  as  fully  as  possible,  a  soft  iron  plug  can  be  machined 
which  will  fit  in  the  opening  left  by  the  drill  after  the  test  is 
completed,  and  if  this  is  solidly  driven  home  but  little  difference 
need  be  expected. 

The  length  of  the  test  bar  is  short,  but  the  character  of  the 
contact  made  by  the  testing  plug  is  exeptionally  good  and  of 
large  area,  so  that  for  high  densities  such  as  are  used  in  practice, 
the  results  obtained  can  probably  be  relied  upon  with  confi- 
dence. 

The  Quantometer. 

Where  ballistic  test  methods  are  used  in  determining  the 
permeability  of  large  masses  of  iron,  some  difficulty  arises 


JPlO.  285. 

in  employing  an  ordinary  ballistic  galvanometer,  as  the  mag- 
netic flux  does  not  instantaneously  attain  its  proper  value  when 
the  current  strength  is  changed  to  a  new  amount.  As  has 
been  explained  in  the  chapter  on  ballistic  galvanometers,  these 
give  correct  indications  only  when  the  duration  of  the  applied 
current  is  so  small  as  compared  with  the  period  of  swing  of 
the  instrument  that  the  former  has  all  passed  before  the  galva- 
nometer needle  has  a  chance  to  make  a  sensible  deflection.  The 
time  required  for  the  attainment  of  the  maximum  flux  value 
in  a  large  mass  of  metal  may  be  as  high  as  thirty  or  even  sixty 
seconds,  which  is  far  too  great  as  compared  with  the  eight  to 
twenty  seconds  period  of  the  ordinary  ballistic  instrument. 


364      ELECTRIC  AND  MAGNETIC  MEASUREMENTS 

To  overcome  this  difficulty,  the  "  quantometer "  has  been 
suggested. 

The  quantometer  is  a  galvanometer  whose  deflections  are  pro- 
portional to  the  quantity  of  electricity  passed  through  it  in  spite 
of  this  long-time  lag.  It  consists  of  a  d'Arsonval  galvanometer 
with  a  pivoted  coil,  like  the  instruments  described  on  pages 
156  to  161,  but  in  place  of  the  volute  springs  which  oppose 
the  coil  motion  it  is  equipped  with  fine  filaments  of  silver  or 
strips  of  phosphor  bronze  such  as  are  used  for  galvanometer 
suspensions  and  which  are  disposed  so  as  to  offer  no  appreciable 
resistance  to  the  coil  motion.  The  windings  are  on  a  short- 
circuited  metallic  frame  like  that  which  serves  to  dampen  the 
indications  of  the  d'Arsonval  instruments  mentioned. 

Without  going  into  the  theory  of  the  instrument,  it  may  be 
stated  that  with  an  apparatus  of  this  nature  the  deflections  are 
proportional  to  the  quantity  of  electricity  that  flows  on  the 
assumption  that  the  pivot  friction  is  negligible,  the  restraining 
force  of  the  conducting  strips  nil,  and  the  duration  of  the  cur- 
rent practically  zero.  A  correction  can,  however,  be  applied  to 
allow  for  the  fact  that  none  of  these  conditions  is  rigidly  correct, 
and  this  feature  admits  of  the  use  of  the  apparatus  for  the  pur- 
pose named.  (See  London  Electrician,  Dec.  26,  1902.) 

TBACTIONAL   METHODS. 

A  magnet  with  its  one  pole  in  contact  with  a  block  of  mag- 
netic material  attracts  the  block  with  a  force  expressed  by  the 
formula  p  =  27rJ2$,  in  which  S  is  the  cross-sectional  area  of  the 
pole  face.  From  this  the  permeability  of  a  given  specimen  can 
be  determined  if  the  magnetizing  force,  If,  is  known,  and  the 
latter  can  be  calculated  from  the  strength  of  the  current  flowing 
and  the  number  of  turns  of  the  magnetizing  coil  by  the  formula 
H  =  4-77  n  i  (for  a  long  coil)  already  given. 

The  formula  expressing  the  value  of  the  permeability  then  is 


J**p 
V  H*s 


1. 


Thompson   Permeameter. 

One    of    the   earliest    permeability    measuring    instruments 
depending  in  principle  on  this  tractive  force  between  a  magne- 


MEASUREMENT  OF  PERMEABILITY. 


365 


tized  bar  and  a  mass  of  magnetized  material  is  the  Thompson 
permeameter.  As  is  shown  in  Fig.  286,  it  consists  of  a  heavy 
rectangular  yoke  of  iron,  having  a  hole  bored  through  one  side, 
through  which  the 
test  rod  passes.  The 
point  on  the  inner 
surface  of  the  oppos- 
ing yoke  against  which 
the  test  bar  rests  is 
carefully  machined  off 
to  have  a  perfectly 
smooth  surface,  and 
the  test  bar  end  is  like- 
wise treated.  It  is 
advisable  to  have  the 


made    slightly    ce//&    H 


w-yya-gVgN  —*' 


Ybffe 

Surfaced 
here 


FIG.  286. 


latter 

conical.  The  magne- 
tizing coil  wound  on  a 
brass  tube  surrounds 
the  specimen  and  is 
itself  so  inclosed  by  the  yoke  that  practically  all  of  the  lines 
of  force  flow  through  the  iron  circuit.  There  is  no  pull  on 
the  test  rod  where  it  passes  through  the  upper  member  of  the 
yoke,  as  the  direction  of  the  lines  of  force  there  is  at  right  angles 
to  it.  By  means  of  a  spring  balance  whose  upper  ring  is 
attached  to  some  hook  that  can  be  gradually  lifted,  the  pull  re- 
quired to  separate  the  test  specimen  from  the  lower  leg  of  the 
yoke  is  read  off  and  the  value  of  the  magnetizing  current  simul- 
taneously read  by  means  of  an  ammeter. 

Thompson  gives  the  following  formula  for  the  permeability : 


(1)  B  =  131T  +  H 


H. 


(2)  B  = 


In  this,  P  is  the  pull  in  pounds  in  the  first  formula  o:  in 
grams  in  the  second,  and  A  the  area  of  contact  of  the  test 
bar  in  square  inches  for  the  first  formula  and  in  square  centi- 
meters for  the  second.  If  the  above  are  compared  with  the  first 
equation  giving  the  portative  power  of  a  magnet  as  above,  they 
will  be  found  to  be  substantially  alike. 


366        ELECTRIC   AND  MAGNETIC  MEASUREMENTS. 

Several  sources  of  error  exist  in  this  apparatus  which  are  of 
such  magnitude  that  it  is  not  suitable  for  work  of  laboratory 
accuracy.  It  can,  however,  be  used  for  demonstration  purposes, 
and  serves  fairly  well  as  a  comparison  instrument  for  comparing 
the  permeabilities  of  a  standard  bar  and  an  approximately  similar 
unknown  one  at  high  flux  densities. 

The  sources  of  error  in  the  tractional  permeameter  are  :  The 
variable  air  gap  where  the  bar  passes  through  the  hole  in  the 
yoke ;  the  uncertainty  of  the  contact  between  the  lower  end 
of  the  bar  and  the  portion  of  the  yoke  on  which  it  rests ;  the 
increasing  leakage  at  the  lower  end  of  the  bar  with  increasing 
magnetization,  which  leakage  lines  are  not  effective  in  increas- 
ing the  force  resisting  separation ;  and  the  fact  that  the  square 


FIG.  287. 


root  of  the  pull  is  involved  in  the  formula  which  makes  a  small 
error  in  observation  of  the  spring  balance  or  in  the  calibration 
of  the  same,  be  a  larger  and  larger  per  cent  as  the  pull  and 
therefore  the  magnetizing  force  decreases. 

The  last  objection  has  so  much  weight  that  in  practice  the 
instrument  cannot  be  used  at  all  for  the  determination  of  per- 
meability at  low  values  of  magnetizing  current. 

Comparative  values  of  specimens  of  metal  for  commercial  use 
can,  however,  be  quickly  measured  by  tractional  permeameters, 
more  particularly  as  these  are  generally  worked  at  high  mag- 
netic densities. 

A  commercial  permeameter  is  shown  in  Fig.  287,  where 
a  spring  put  in  tension  by  turning  the  hand  crank  shown 


MEASUREMENT  OF   PERMEABILITY. 


367 


measures  the  force  required  to  separate  the  specimen  from  the 
yoke. 

Another  tractional  permeameter  is  shown  in  Fig.  288.  Here 
sand  is  allowed  to  flow  through  the  pipe,  T,  into  a  bucket,  P, 
until  the  test  speci- 
men is  torn  away, 
whereupon  the  flow 
of  sand  is  at  once  cut 
off  and  the  weight 
subsequently  ascer- 
tained. 


Ewing  Balance. 

In  this  instrument 
for  measuring  per- 
meability by  t  r  a  c- 
tional  force,  an  effort 
is  made  to  eliminate 
the  error  due  to  the 
variable  contact  be- 
tween the  test  speci- 
men and  the  mass  of 

metal  closing  the  magnetic  circuit  by  the  expedient  shown  in 
Fig.  289.  The  test  bar,  E,  is  made  circular  in  section  as  usual, 
and  one  of  its  ends  rests  in  a  V-shaped  notch  cut  in  one  end 
of  the  iron  spool  about  which  the  magnetizing  coil,  B,  is 
wound,  the  other  end  resting  on  a  rounded  surface  at  the  other 
end  of  the  spool,  as  shown  at  a.  The  contact  between  E  and 


FIG.  288. 


a  is  necessarily  a  point,  being  the  contact  between  two  cylin- 
drical surfaces  at  right  angles  to  each  other. 

The  V-shaped  depression  in  which  the  end  of  the  specimen 
E  rests  forms  a  kind  of  a  hinge,  so  that  when  a  lifting  force  is 
applied  by  the  steel  yard  arrangement,  F,  a  alone  is  raised.  The 


368       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

force  tending  to  tear  the  test  specimen  away  from  the  magnet- 
izing block  is,  of  course,  obtained  by  sliding  the  weight,  P,  out 
along  the  graduated  arm  of  the  steel  yard. 

In  the  commercial  use  of  this  device  the  current  strength  is 
not  fixed  by  means  of  an  ammeter,  but  a  standard  bar  is  first 
inserted,  and  the  current  varied  until  it  just  lets  go  for  a  pre- 
determined position  of  P.  The  test  bar  is  then  substituted  for 
the  standard  and  the  position  of  P  which  causes  this  to  be 
pulled  away,  is  noted.  The  steel  yard  is  graduated  directly  in 
gausses  and  forms  a  convenient  although  somewhat  crude 
arrangement  for  some  workshop  tests. 

ATTBACTIONAL   METHODS. 

Du  Bois  Magnetic  Balance. 

In  this  instrument  the  test  specimen,  D,  Fig.  290,  is  usually 
made  a  rod  about  15  centimeters  long.  By  means  of  clamps  its 


y/////////////////////////////. 


FIG.  290. 

ends  are  brought  into  close  contact  with  heavy  iron  pole  pieces,  P 
and  P,  and  the  magnetic  circuit  is  completed  through  these,  the 
air  gaps,  J^and  E,  and  the  heavy  yoke,  F.  The  magnetizing  sole- 
noid, J5,  surrounds  the  specimen.  F  is  provided  with  a  pair  of 
knife  edges  located  opposite  to  one  another  at  the  point,  A,  the 
peculiar  distribution  of  metal  shown  by  the  figure  being  such 
that  the  yoke  is  balanced  around  A  by  the  weights  of  the  two 
ends.  When  current  is  passed  through  B  the  force  of  magnetic 
attraction  at  each  of  the  faces,  E  and  E,  is  evidently  the  same, 
but  as  the  pull  through  the  left-hand  gap  acts  on  a  longer  lever 
arm,  the  yoke,  P,  will  tend  to  descend  at  that  end. 

This  force  is  balanced  by  moving  the  small  sliding  weight 


MEASUREMENT  OF  PERMEABILITY.  369 

shown  in  Fig.  291  along  the  top  of  the  yoke.  Limiting  stops 
are  placed  at  each  end  of  the  yoke,  one  of  them,  as  is  shown  to 
the  left  in  Fig.  290,  being  usually  provided  with  a  pair  of  plat- 
inum contacts  connected  in  circuit  with  a  battery,  and  a  galva- 
nometer or  bell,  so  that  if  that  yoke  end  descends  appreciably  be- 
low the  normal  position,  a  warning  is  instantly  given. 

The  attraction  of  the  pole  pieces  on  the  yoke  varies  as  the 
square  of  the  flux  through  the  magnetic  circuit,  and  for  a  given 
magnetizing  current  the  graduated  scale  alongside  of  which  the 
movable  weight  slides  may  therefore  be  calibrated  directly  in 


FIG.  291. 

gausses,  the  proper  allowance  for  the  reluctance  of  the  pole 
pieces,  the  air  gaps,  and  the  yoke  having  first  been  experiment- 
ally determined  and  allowed  for. 

The  reluctance  of  the  air  gaps  in  this  instrument  is  so  great 
as  compared  with  that  of  the  resistance  of  the  rest  of  the  circuit 
that  small  variations  in  the  resistance  of  the  joints  between  the 
test  specimen  and  the  pole  pieces  introduces  no  material  error. 

DEFLECTIOXAL   METHODS. 

If  a  known  current  is  passed  through  the  movable  coil  of  any 
of  the  d'Arsonval  types  of  instruments  previously  described, 
the  deflection  of  the  needle  attached  thereto  will  be  in  propor- 
tion to  the  strength  of  the  magnetic  field  in  which  the  coil 


370      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


works.  The  flux  that  forms  this  field  is,  for  a  given  strength 
of  current  through  a  solenoid  surrounding  an  iron  core  to  whose 
ends  are  attached  the  pole  pieces  between  which  the  coil  swings, 
proportionate  to  the  permeability  of  the  core.  Instruments  for 
the  measurement  of  permeability  based  on  this  principle  may 
conveniently  be  termed  of  the  deflectional  type. 

Koepsel  Permeameter. 

This  prominent  instrument   based  on  the  above  deflectional 
method  is  shown  in  section  in  Fig.  292.    The  test  bar,  E,  is  placed 

within  the  magnetizing  coil, 
B,  and  firmly  clamped  in 
place  by  means  of  thumb 
screws  to  eliminate  as  far  as 
possible  errors  due  to  the 

i°ints-  The  heavy iron  p°le 

pieces,  JJ,  embrace  the  mov- 
able coil,  5,  and  to  the  latter 
is  attached  a  pointer  which 
swings  over  a  scale  graduated 
directly  in  gausses.  In  mak- 
ing a  test  current  of  a  known  value  is,  sent  through  b  and  the 
deflection  corresponding  to  different  strengths  of  current  through 
B  noted.  The  complete  apparatus  is  illustrated  in  Fig.  293, 
the  batteries  being  shown  behind  the  instrument  and  the  rheo- 


FIG.  292. 


FIG.  293. 


stats  for  regulating  the   strength  of    the  current  through  the 
magnetizing  coil  and  the  moving  coil  respectively  to  the  right 


MEASUREMENT  OF  PERMEABILITY. 


371 


and  left  of  it.  The  batteries  supply  the  current  for  b  only, 
that  necessary  for  B  being  drawn  from  a  separate  source,  usually 
storage,  batteries,  and  measured  by  a  separate  ammeter. 

Carpentier  Permeameter. 

This  instrument  shown  diagrammatically  with  its  accompany- 
ing connections  in  Fig.  294,  and  in  perspective  in  Fig.  295,  is 
somewhat  similar  to  the  Koepsel  device,  but  the  flux  through 
the  heavy  iron  yoke  pieces  that  complete  the  magnetic  circuit 
is  measured  in  another  way.  As  is  shown  in  Fig.  294,  a  small 
rectangular  gap  is  left  at  the  points  of  junction  of  the  two  yokes, 
in  the  upper  one  of  which  there  is  freely  suspended  a  short  mag- 
netic needle.  When  a  flux  passes  through  the  yoke  the  needle 
of  course  tends  to  place  itself  parallel  to  the  lines,  and  the 


FIG.  294. 

needle  attached  thereto  which  can  be  seen  inside  of  the  little 
rectangular  box  on  top  of  the  apparatus  in  Fig.  295  is  deflected. 
By  turning  the  knurled  head  shown  in  the  same  figure  a  spring 
is  wound  up,  which  as  in  the  electro  dynamometer  (see  page  165) 
introduces  a  measureable  opposing  force  and  brings  the  needle 
back  to  its  original  position  again.  The  angle  of  twist  of  the 
knurled  head  required  to  bring  the  index  to  the  zero  mark  is  for 
«ach  value  of  the  magnetizing  current,  a  measurement  of  the 
flux  through  the  yokes,  and  the  permeability  of  the  test  speci- 
men can  therefore  be  determined  by  reference  to  a  calibration 
curve  which  accompanies  the  apparatus. 

BRIDGE   METHODS. 

Various  magnetic  analogues  of  the  Wheatstone  Bridge  have 
been  proposed  and  constructed  from  time  to  time.     The  origi- 


372       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

nator  of  the  plan  seems  to  have  been  Ewing,  whose  bridge  is 
shown  in  Fig.  296.  Two  bars  of  identical  dimensions  are  em- 
ployed, one  of  them,  A,  being  a  standard,  and  the  other  the  one 
whose  permeability  is  to  be  measured.  The  ends  of  these  bars 
are  clamped  into  heavy  iron  yokes,  (7(7,  and  a  pivoted  magnet- 
ized needle,  #,  placed  between  their  extremities  serves  to  indi- 
cate whether  these  yokes  are  magnetized.  The  bar,  5,  shown 
is  a  short  permanent  magnet  which  is  used  to  give  directive 
force  to  the  pivoted  needle. 

A  and  B  are  surrounded,  each  with  its  own  magnetizing  coil, 
the  two  being  connected  in  series,  but  opposed  so  that  the  direc- 


FiG.  295. 

tion  of  flux  through  the  one  is  opposite  to  that  in  the  other. 
The  number  of  turns  around  the  standard  specimen  is  fixed,  but 
that  around  B  is  variable  by  means  of  a  contact  arm  whose  end 
can  be  moved  over  a  row  of  contacts  connected  to  different 
turns  of  the  winding.  This  contact  arm  device  is  equipped 
with  auxiliary  resistances,  so  that  each  time  a  coil  is  cut  out  of 
the  magnetizing  circuit  an  equivalent  resistance  is  added  to  the 
circuit,  so  that  the  strength  of  the  current  flowing  remains 
uniform. 


MEASUREMENT  OF  PERMEABILITY. 


373 


When  the  flux  through  each  specimen  is  the  same,  the  path 
of  the  lines  of  force  is  evidently  along  one  and  back  through  the 
other,  none  being  com- 
pelled to  flow  through  the 
yokes  and  across  the  gap. 
No  deflection  of  the  nee- 
dle, a,  thus  means  that 
the  fluxes  are  the  same. 
In  practice  the  number  of 
turns  surrounding  the  test 
bar  is  varied  until  the 
needle,  a,  no  longer  shows 
a  permanent  deflection 
with  the  current  flowing 
in  one  direction  or  the 
other,  whereupon  it  is 
known  that  the  fluxes 
furnished  by  the  two  speci- 
mens are  alike  since  they 
neutralize  each  other. 
Their  permeabilities  are 
hence  in  the  ratio  of  the 
turns.  To  obtain  the  complete  permeability  curve  the  strength 
of  the  current  being  used  must  be  measured  by  means  of  an 
ammeter  and  successive  readings  made  for  different  values. 

MISCELLANEOUS   METHODS. 

The  large  errors  introduced  by  the  variable  value  of  the  con- 
tact between  a  test  specimen  and  the  heavy  iron  yokes  used  in 
most  permeameters  has  led  to  many  attempts  to  devise  some 
satisfactory  method  that  will  give  results  which  are  independent 
of  this  element. 

One  of  the  early  ones  is  due  to  Ewing  and  operates  as 
follows : 

Referring  to  Fig.  297,  A  is  a  standard  bar  and  B  the  one 
to  be  measured.  Holes  are  drilled  in  the  iron  yokes,  0  and  D, 
into  which  these  bars  fit  snugly,  the  contact  being  made  as  solid 
as  possible  by  means  of  the  clamp  screws.  Solenoids  through 
which  are  passed  the  magnetizing  current  surround  both  test 
specimens  and  are  made  of  a  length  that  just  fits  between  0 


FlG.  296. 


374       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

and  D  with  these  in  the  position  shown  in  the  figure.  An  ex- 
ploring coil  surrounds  one  of  the  solenoids  and  the  value  of  the 
flux  through  B  is  found  in  terms  of  that  through  A  by  a  method 
similar  to  that  used  in  the  Rowland  test  before  described.  The 
magnetic  circuit  in  this  case  evidently  includes  the  reluctances 
of  the  bars  A  and  B  plus  that  of  the  yokes,  O  and  D,  plus  that 
of  the  four  joints  between  the  bar  ends  and  the  yokes.  After 
making  a  determination  with  the  yoke,  D,  located  as  illustrated, 
the  clamp  screws  holding  it  to  the  bars  are  loosened  and  the 
yoke  slides  along  to  a  new  position.  The  test  is  repeated  there, 
and  from  this  and  the  preceding  one  the  induction  in  the  test 
specimen  is  calculated.  As  the  contacts  between  the  }7oke,  C, 
and  the  two  bars  are  undisturbed  their  reluctance  and  that  of 
the  yoke  is  eliminated.  The  same  thing  holds  good  of  the  re- 
luctance of  the  yoke,  D,  so  that  the  result  is  correct  if  the  \nag- 


'A 

U 

c 

D 

1 

B 

i           1 

:      i     i 

FlG.  297. 

netic  resistance  of  the  joints  between  A  and  D  and  B  and  D  is 
the  same  in  the  first  position  of  D  as  in  the  second. 

It  is  unfortunate  that  this  last  assumption  is  not  entirely 
valid  and  that  the  arrangement  therefore  gives  permeability 
values  which  while  amply  close  for  practical  purposes  at  high 
magnetic  densities  are  not  sufficiently  exact  for  accurate  work 
or  at  low  densities. 

Picou  Permeameter. 

In  this  instrument  devised  by  Picou  and  modified  by  Armag- 
nat,  the  method  of  eliminating  the  errors  due  to  the  variable 
resistance  of  the  magnetic  joints  is  entirely  different 

Referring  to  Fig.  298,  the  test  specimen,  6,  is  made  rectangu- 
lar and  may  take  the  form  of  a  prism  of  solid  metal  or  of  several 
layers  of  sheet  iron  such  as  is  used  for  transformer  and  arma- 
ture work.  There  are  two  yokes,  B,  B2  respectively,  which  are 


MEASUREMENT  OF  PERMEABILITY. 


375 


/M, 


111 


M 


U  shaped  and  between  the  ends  of  whose  legs  the  test  specimen 
is  inserted.     Magnetizing  coils  surround  all  three  as  shown  and 
suitable  resistances,  R^  R^  are  inserted  in  the  yoke  and  test 
specimen    circuits,  so 
that  the  strength    of 
the    current    flowing 
through  them  may  be 
varied  at  will. 

The  measurement 
of  the  permeability  of 
b  involves  two  steps. 
First  of  all,  current  is 
sent  through  the  sole- 
noids surrounding  the 
yokes  in  such  a  direc- 
tion that  the  resultant 
magnetic  fluxes  form 
a  closed  path  through 
the  yokes  only,  as  is 
shown  by  the  dotted 
lines  in  Fig.  299. 
Under  these  circum- 
stances it  is  clear  that 
there  is  no  flux 
through  the  bar,  5, 

itself,  and  that  the  reluctance  of  the  magnetic  circuit  is  that  of 
the  material  composing  the  yokes  plus  that  of  the  four  joints 
between  the  test  specimen  faces  and  the  yoke  ends,  plus  the 
reluctance  of  those  portions  of  the  length  of  the  test  bar, 
lettered  e  and  a  respectively,  in  Fig.  299. 

Suppose  that  under  these  conditions  the  flux  through  the 
circuit  is  ascertained  by  making  a  ballistic  test  or  in  any 
other  convenient  manner.  The  permeability  of  the  circuit  can 
then  be  calculated  from  the  magnetizing  force  due  to  the  meas- 
ured current  through  the  exciting  solenoids  in  the  ordinary 
way. 

The  electrical  connections  are  then  changed  so  that  uie  direc- 
tion of  the  current  in  one  or  the  other  of  the  exciting  solenoids 
is  reversed,  with  the  result  that  the  flux  directions  through 
BI  B2  are  opposite,  as  shown  in  Fig.  300.  The  magnetic  circuit 


FIG.  298. 


376      ELECTRIC   AND  MAGNETIC  MEASUREMENTS. 


X- 

I 

1 

EHxji 

\ 

c                     b                   a 

l 
A 

1 

i 

\ 

lEjEBE—- 

FIG.  299. 


for  each  yoke  is  then  completed  through  the  test  specimen,  and 
as  the  reluctance  of  this  circuit  is  greater  than  the  first  by  that 

of  the    specimen 

^ ^ X-K/  for   its  length,   e, 

the  flux  through 
both  Bl  and  B2 
is  lessened.  By 
passing  current 
through  the  sole- 
noid surrounding 
the  test  specimen 
in  the  proper  di- 
rection a  magneto- 
motive force  is  set 
up,  which  can  be 
adjusted  by  ma- 
_  stipulating  the 
rheostat,  R^  Fig. 
298,  until  the  flux  through  Bl  and  B2  becomes  again  what  it 
was  under  the  conditions  in  Fig.  299. 

The  reluctance  of  the  test  specimen  may  then  be  calculated 
directly  from  the 
strength  of  the 
current  that  must 
be  passed  through 
its  surrounding 
solenoid  to  bring 
about  the  above 
state  of  affairs, 
for  the  magneto- 
motive force  that 
the  coil  must  sup- 
ply is  just  that 
required  to  force 
the  known  flux 
through  the  speci- 
men, that  required  to  overcome  the  reluctance  at  the  joints 
having  been  accounted  for  in  the  first  measurement.  Knowing 
the  strength  of  the  current  around  b  and  the  number  of  turns  in 
its  solenoid,  the  magnetizing  force,  and  therefore  finally  the 
permeability,  may  be  determined  direct. 


""*\  ~   ~   ~r 

1 

~^~Y~\~\~ 

^ 

\ 

\ 
\ 

<  €       > 

1 

1 
1 

1 

b~ 

"Yiife-fiz 

-' 

\ 

—j    u  L  v,  ^ 

\ 

\ 

\ 

1 

\ 

EEEQE 

1 

*s                    ^^ 

FIG.  300. 

MEASUREMENT  OF  PERMEABILITY. 


377 


Owing  to  the  great  superiority  of  zero  methods  of  measure- 
ment over  methods  involving  values  of  deflection,  considerable 
thought  has  been  devoted  to  modifying  this  Picou  apparatus  to 
bring  it  into  this  category.  As  a  result  it  is  now  generally 


FIG.  sou 


supplied  arranged  as  follows  :  As  shown  in  Fig.  301,  a  fine  wire 
winding  acting  as  an  exploring  coil  surrounds  each  yoke  and 
the  test  specimen.  An  auxiliary  transformer,  T,  is  also  employed 
which  is  energized  by  being  placed  in  series  with  the  magnetiz- 


FIG.  302. 


ing  windings  surrounding  the  yokes  and  whose  transformation 
ratio  may  be  manually  adjusted  at  will.  The  secondary  circuit 
of  the  auxiliary  transformer  is  completed  through  the  two 


378      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

exploring  coils  on  the  yokes,  connections  being  made  so  that  the 
E.M.F.'s  induced  therein  are  opposite  to  that  induced  in  the 
coils.  It  can  readily  be  seen  that  by  suitably  adjusting  the  trans- 
formation ratio  of  T  the  effect  on  a  galvanometer,  6r,  inserted 
in  the  coil  circuit  may  be  made  zero ;  the  fact  that  equilibrium 
has  been  thus  attained  must  be  carefully  established  by  several 
reversals  of  the  direct  magnetizing  current. 

To  determine  the  flux  in  the  bar,  £,  after  the  electrical  con- 
nections are  changed  so  that  the  magnetic  circuit  is  completed 
through  it,  a  special  commutator  is  employed,  which  cuts  the 
solenoids  of  B\  and  B?  out  of  circuit  at  the  same  time  that  5's 


.  303. 


solenoid  is  inserted.  The  discharge  through  6's  test  coil  circuit 
is  passed  through  a  ballistic  galvanometer,  whose  scale  may  be 
calibrated  directly  in  gausses. 

The  portion  of  the  instrument  containing  the  two  yokes  with 
their  soils  plus  the  commutator  and  reversing  switch  is  shown 
in  Fig.  302,  that  of  the  portion  of  the  apparatus  including  the 
rheostat  and  galvanometer  being  illustrated  by  Fig.  303. 

It  is  claimed  that  the  results  obtained  with  this  device  are  of 
the  highest  accuracy  and  that  the  elimination  of  the  resistance 
at  the  joints  is  so  far  successful  that  a  practically  identical  set 
of  readings  is  obtained  for  a  given  stack  of  sheet  iron  strips  for 
the  order  in  which  they  are  first  placed  in  the  apparatus  and  that 


MEASUREMENT  OP  PERMEABILITY. 


379 


which  they  show  when  subsequently  removed,  mixed  up  at  ran- 
dom, and  then  replaced. 

Burger  Permeameter. 

This  device,  while  probably  not  capable  of  giving  as  accurate 
results  as  the  preceding,  is  in  quite  extended  use  and  has  the 
advantage  of  giving  the  results  very  rapidly.     In  it  the  test  bar 
is  cut  in  half  and  mounted 
on  a  heavy  iron  yoke  in  a 
manner  somewhat  similar 
to    that  employed  in  the 
Hopkinson     divided     bar 

apparatus.  The  magnetizing  coil  surrounds  the  specimen  in 
the  same  way  also,  but  instead  of  having  a  snap  coil  in  the  gap 
between  the  bar  ends,  a  bismuth  spiral  is  inserted,  as  is  shown 
in  Fig.  304.  The  variations  in  electrical  resistance  of  this 
spiral  form  a  measure  of  the  strength  of  the  field  in  which  it  is 
placed  (see  page  350)  and  hence  of  the  permeability  of  the  rod 
undar  test. 

As  made  by  Hartmann  and  Braun,  the  Burger  permeameter 
is  made  one  self-contained  piece  of  apparatus,  as  is  illustrated  in 
Fig.  305,  and  includes  the  yoke  with  its  clamps,  magnetizing 


FIG.  305. 

coil,  and  bismuth  spiral;  two  slide-wire  bridges,  one  to  make 
temperature  corrections  and  the  other  for  measuring  the  resis- 
tance of  the  spiral ;  a  galvanometer  for  use  with  the  bridge  ;  an 
ammeter  for  measuring  the  exciting  current;  a  combination 
galvanometer  and  battery  key  for  the  bridge,  and  a  reversing 
switch  for  the  energizing  circuit. 


CHAPTER   IV. 


HYSTERESIS. 


IF  we  start  with  a  completely  demagnetized  iron  specimen 
and  draw  its  permeability  curve  by  any  of  the  methods  just 
given  the  curve  will,  as  has  been  explained,  take  the  form  shown 
by  the  solid  line  in  Fig.  306.  If  after  the  maximum  desired 
value  of  H  has  been  been  attained  the  exciting  current  is 


(B 

16000 
15000 
14000 
19000 
12000 
11000 
10000 
9000 


7000 


€000 

eooo 

400C 

sooc 


JOOO 


14   16  41  _*0   *3   21  26  28   80 
FIG.  306. 

decreased  step  by  step,  the  values  of  B  corresponding  to  those  of 
If  will  no  longer  coincide  with  those  found  in  the  initial  test, 
but  will  give  a  set  of  readings  which  when  plotted  will  form 
the  dotted  curve  in  the  same  figure.  If  the  direction  of  H  is 
now  reversed,  the  value  of  B  will  continue  decreasing  until  it 
comes  to  zero  and  will  then  itself  reverse  in  direction  until 

380 


HYSTERESIS.  381 

a  maximum  negative  value  is  attained  which  will  be  found  equal 
to  the  positive  value  corresponding  to  the  same  maximum  posi- 
tive value  of  H.  If  H  is  then  brought  back  to  zero,  reversed, 
and  then  increased,  again  a  similar  curve  will  be  given  which 
will  join  the  first  when  H  has  reached  its  first  positive  maximum 
value.  The  curves  form  a  closed  figure  shown  in  Fig.  307,  which 
is  known  as  the  hysteretic  loop.  It  will  be  retraced  as  often  as 
the  magnetizing  force  is  made  to  go  through  the  same  cycle  of 
changes  in  strength.  The  shape  of  the  loop  depends  not  only 
on  the  metal  under  test,  but  its  physical  condition,  being,  for 
instance,  much  more  elongated  and  of  larger  area  for  a  hard 
tempered  piece  of  steel  than  for  one  cut  from  the  same  specimen 
that  was  subsequently  carefully  annealed.  It  can  be  shown  that 
if  the  value  of  B  in  Fig.  307  is  expressed  in  lines  of  force,  and 
that  of  H  in  tens  of  amperes,  the  area  of  the  hysteresis  loop  is 
the  energy  in  ergs  required  to  force  the  metal  to  overcome  the 
cycle  of  changes. 

Also  it  has  been  found  that  for  a  given  specimen  and  form 
of  wave  of  the  exciting  current,  the  area  of  the  loop  is  the  same 
whether  the  successive  reversals  in  flux  succeed  one  another 
with  the  lowest  frequency  found  in  commercial  apparatus  or  the 
highest  frequency. 

The  predetermination  of  the  amount  of  energy  consumed  by 
hysteresis  is  a  most  important  requirement  in  the  design  of 
much  electrical  machinery. 

MEASUREMENT    OF    HYSTERETIC    LOSSES. 

Method  of  Plotting   Curves. 

A  very  obvious  method  of  determining  the  hysteretic  loss  is 
to  draw  the  complete  loop  from  successive  observations  made 
with  differing  magnetizing  forces  by  any  of  the  permeability 
measuring  plans  spoken  of,  and  then  to  obtain  the  area  of  the 
resultant  loop  with  the  aid  of  a  planirneter.  Just  as  obviously, 
however,  this  method  is  exceedingly  tedious  because  of  the 
large  number  of  observations  required,  and  it  is  therefore  seldom 
used  in  the  workshop. 

Wattmeter  Method. 

The  energy  consumed  in  the  hysteretic  cycle  may  be  measured 
very  simply  by  using  a  sensitive  indicating  wattmeter.  For  this 


382      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 


test  the  specimen  is  surrounded  with  a  magnetizing  coil  and 
the  energy  expended  therein  measured,  first  with  the  specimen 
removed,  and  afterward  with  it  in  position.  The  first  reading 
gives  the  energy  required  to  overcome  the  resistance  of  the 
magnetizing  coil  itself,  and  the  second  that  energy  plus  that 
expended  by  hysteresis  and  eddy  currents.  As  it  is  difficult  to 
determine  the  latter  separately  this  meter  test  is  usually  used 


-06 


>R 


(B- 


* 

47 


+8000 


t6000 


44000 


JC 


FIG.  307. 


only  when  it  is  possible  to  obtain  the  specimen  in  the  form  of 
thin  sheets,  which  may  be  electrically  insulated  from  one  another 
by  varnishing  or  otherwise,  thus  practically  eliminating  the 
eddy  current  loss. 

Instead  of  connecting  the  wattmeter  in  the  usual  way,  it  is 
advisable  to  have  two  windings  over  the  specimen,  one  of  wire 
through  which  the  magnetizing  current  flows,  and  the  other  of 


HYSTERESIS. 


383 


fine  wire  insulated  from  the  first,  and  in  which  there  is  generated 
by  the  alternating  flux  an  E.M.F.  that  is  applied  to  the  poten- 
tial circuit  of  the  wattmeter.  This  eliminates  the  error  due  to 
the  energy  loss  in  the  coil.  Connections  of  this  kind  are  shown 
in  Fig.  308,  where  there  is  added  also  an  ammeter  and  a  volt- 
meter. The  two  latter  instruments  are  useful  for  determining 
the  magnetomotive  force  and  the  flux  respectively. 

Ewing  Hysteresis  Meter. 

The  hysteretic  loss  in  a  given  specimen  is  the  same  whether 
the  alternations  in  the  field  strength  are  caused  by  rotating 
it  through  a  field  or  holding  it  stationary  and  reversing  the 
direction  of  the  current  through  the  exciting  coil.  It  is  also 


FIG.  308. 

the  same  whether  the  specimen  is  held  stationary  and  the  field 
rotated  or  vice  versa. 

One  of  the  best  known  hysteretic  loss  meters  is  the  Ewing, 
which  is  based  on  the  latter  principle  and  constructed  as  shown 
in  Fig.  309.  In  it  a  C-shaped  permanent  magnet  is  supported 
by  knife  edges  on  agate  bearings,  and  between  its  polar  extremi- 
ties there  is  placed  a  clamp  to  hold  the  test  specimen.  This 
whole  clamp  may  be  rapidly  rotated  by  means  of  the  hand  wheel, 
and  when  this  is  done  the  reaction  between  the  field  of  the 
specimen  and  that  of  the  magnet  tends  to  carry  the  latter 
along  in  the  same  direction,  this  motion  being  opposed  by  suit- 
able counterweights  and  indicated  by  a  needle  sweeping  over 
a  stationary  scale.  To  the  lower  part  of  the  magnet  is  fixed  a 


384      ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

flat  vane  dipping  into  an  oil    bath    which    dampens  the  indi- 
cations. 

Two  standard  specimens  are  supplied  with  each  instrument 
and  the  deflections  that  these  give  are  noted  before  any  test  is 
started.  These  two  values  are  used  to  establish  a  curve  show- 
ing the  relation  between  the  deflection  and  the  hysteretic  losses, 
so  that  when  the  unknown  specimen  is  inserted  the  hysteresis 
loss  can  be  found  from  the  deflection  by  referring  to  the  curve. 


FIG.  309. 


The  sample  must  be  laminated  in  order  to  avoid  eddy  cur- 
rents, but  it  is  claimed  that  the  thickness  to  which  they  are 
piled  up  has  such  a  small  affect  that  within  the  limit  allowed  by 
the  clamps  no  correction  need  be  applied. 

Professor  Ewing  has  recently  determined  that  the  hysteretic 
loss  in  the  standard  test  specimens  does  not  remain  constant 
indefinitely,  and  it  is  hence  advisable  to  primarily  determine  the 
value  of  that  of  the  standard  by  some  other  method  if  the  appa- 


HYSTERESIS. 


385 


ratus  is  to  be  used  for  exact  determinations.  This  refinement  is 
however  not  necessary  in  workshop  practice,  because  compari- 
tive  results  are  as  a  rule  all  that  is  desired. 

Blondell  Hysteresis  Meter. 

In  this  instrument,  which  is  shown  in  section  in  Fig.  310,  the 
test  specimen  is  made  in  the  form  of  a  ring  which  is  secured  to 


FIG.  310. 

a  support  that  can  be  rotated  about  the  central  axis  of  the  device. 
The  tendency  to  rotate  is  balanced  by  means  of  the  spring 
shown,  and  a  needle  attached  to  the  frame  carrying  it  is  brought 
back  to  a  zero  mark  by  turning  a  knurled  head  as  in  a  dynamo- 
meter. The  rotating  magnetic  field  is  supplied  by  the  U-shaped 
magnet,  and  its  torque  as  indicated  by  the  position  of  the  torsion 
head  is  a  measure  of  the  hysteretic  loss. 

Holden  Instrument. 

Another  hysteresis  meter,  used  by  the  General  Electric  Com- 
pany and  employing  a  cylindrical  test  specimen  in  a  rotary  field, 
is  shown  in  Fig.  311.  The  magnet  is  here  an  electromagnet, 


386       ELECTRIC  AND  MAGNETIC  MEASUREMENTS. 

current  being  passed  through  its  winding  with  the  aid  of  two 
collector  rings  like  those  of  an  alternating  current  generator. 
The  arrangement  for  measuring  the  torque  of  the  sample  is 
the  same  dynamometer  spring  affair,  the  values  of  the  torque 
being  read  off  from  the  position  of  a  movable  index  relative  to  a 
fixed  scale. 

In  this  instrument  provision  is  made  also  for  the  measurement 
of  the  flux,  this  being  done  as  follows :  A  coil  surrounds  but 
does  not  touch  the  test  ring  and  rotates  with  it.  It  has  its  ter- 
minals connected  to  a  two-part  commutator,  so  that  it  delivers 
direct  current  to  a  pair  of  binding  posts  that  are  connected  to 
the  brushes.  A  voltmeter  attached  to  the  binding  posts  then 
shows  the  magnetic  induction  as  the  number  of  turns  in  the 
exploring  coil,  the  cross-section  of  the  test  specimen,  the  speed 
of  rotation  of  the  magnet,  and  the  resistance  of  the  circuit  com- 
prising the  voltmeter,  test  coil,  and  con- 
nections are  all  known.  The  test  coil 
feature  is  a  most  convenient  one,  as  by 
its  aid  the  induction  in  the  specimen  can 
be  read  in  each  instance  and  of  course 
readily  adjusted  to  any  desired  value  by 
varying  the  strength  of  the  exciting  cur- 
rent. It  is  claimed  that  the  most  impor- 
tant reason  for  not  adopting  the  Ewing 
FIG  sii.  P^an  °^  employing  a  rotating  permanent 

magnet  in  place  of  the  electromagnet  is 

that  with  the  former  results  obtained  on  specimens  of  iron  of 
widely  different  character  were  not  correct. 

Searle  Method. 

A  very  elegant  method  for  measuring  the  hysteretic  loss  for 
a  single  magnetizing  cycle  has  been  proposed  by  Searle,  and 
involves  the  use  of  an  instrument  that  is  practically  a  ballistic 
wattmeter.  As  is  shown  by  the  diagrammatic  sketch  in  Fig.  312, 
the  test  specimen,  E,  is  placed  inside  of  a  solenoid,  the  series  coil, 
of  the  wattmeter  being  connected  in  series  with  this  winding. 
Another  coil  surrounds  the  first,  and  to  its  terminals  is 
connnected  the  potential  coil  of  the  wattmeter. 

To  the  terminals,  A  and  B,  of  the  magnetizing  coil  there  is 
connected  a  reversing  commutator,  so  that  the  current  sent 


HYSTERESIS. 


387 


through  it  and  whose  value  is  measured  by  an  ammeter  can  be 
suddenly  reversed  in  direction.  The  electro-motive  force  induced 
in  the  secondary  winding  is  proportional  to  the  rate  of  change 


FIG.  312. 
in  flux  through  the  core,  that  is,  to  — 

(JLL 


The  current  through 


the  primary  winding  at  this  instant  is  Hdt,  so  that  the  couple 
deflecting  the  wattmeter  is  Hdt  -=-  •     This  integrated    shows 

that  the  deflection  of  the  instrument  is  proportional  to  HB,  that 
is  to  say,  to  the  hysteretic  loss. 

It  is,  of  course,  assumed  that  the  reversal  is  made  so  quickly 
that  the  whole  cycle  has  been  completed  before  the  galvanometer 
has  a  chance  to  make  a  sensible  deflection. 


APPENDIX. 

THE  following  list  is  intended  to  serve  as  a  general  guide  to 
those  who  desire  to  ascertain  where  they  may  procure  instru- 
ments and  devices  of  the  types  described  in  this  volume,  or  to 
obtain  from  the  makers  thereof  more  detailed  information  as  to 
construction  or  operation  than  has  found  place  in  a  treatise  of 
the  necessarily  general  nature  of  this  one.  It  is  not  contended 
that  the  list  is  complete,  in  fact  it  would  hardly  be  feasible  in 
many  instances  to  ascertain  and  record  each  maker  of  each  form 
of  device,  but  it  is  thought  that  it  will  be  found  accurate  as  far 
as  it  goes  and  should  certainly  serve  a  useful  purpose.  In  those 
cases  where  the  manufacturer  is  located  abroad,  the  endeavor 
has  been  made  to  give  the  name  of  the  United  States  represen- 
tative of  the  line  as  well  as  his  own  so  as  to  enable  those  inter- 
ested to  promptly  communicate  with  the  nearest  authoritative 
source. 

The  schedule  is  arranged  in  the  order  of  the  serial  numbers 
of  the  illustrations  to  facilitate  reference  thereto.  Where  an 
illustration  is  not  mentioned  by  a  number  in  the  list  and  is  not 
simply  diagrammatic  or  illustrative  of  a  principle,  it  may  usually 
be  taken  for  granted  that  the  apparatus  is  of  a  special  or  labor- 
atory character,  built  to  order  only,  and  about  which  a  specialist 
in  fine  instrument  building  should  hence  be  consulted  if  it  is 
desired  to  procure  the  actual  apparatus. 

LIST  OF  ABBREVIATIONS  EMPLOYED. 

A.  E.  G.  Allgemeine  Elektricitats  Ges.,  Berlin,  Germany. 

B.  Co.  Bristol  Company,  Waterbury,  Conn. 

C.  &  A.  Chauvin  and  Arnoux,  Paris,  France. 

C.  &  Co.  Crompton  and  Company,  London,  England. 

C.  O.  C.  Ollivetti,  Milan,  Italy. 

C.  S.  I.  Co.  Cambridge  Scientific  Inst.  Co.,  Cambridge,  England. 

D.  E.  M.  Co.  Duncan  Electric  Mfg.  Co.,  Lafayette,  Ind. 

D.  M.  Co.  Diamond  Meter  Co.,  Peoria,  111. 

E.  B.  Elliott  Bros.,  London,  England. 

E.  D.  Co.  Electro  Dynamic  Co.,  Bayonne,  N.  J. 

E.  E.  M.  Co.         Edison  Electric  Mfg.  Co.,  Orange,  N.  J. 
E.  V.  B.  E.  V.  Baillard,  New  York,  N.  Y. 

389 


390  APPENDIX. 

F.  P.  Co.  Foote,  Pierson  &  Co.,  New  York,  N.  Y. 

F.  W.  E.  Co.  Fort  Wayne  Elect.  Co.,  Fort  Wayne,  Ind. 

G.  E.  Co.  General  Electric  Co.,  Schenectady,  N.  Y. 

G.  I.  Co.  General  Inc.  Arc.  Light  Co.,  Pittsfield,  Mass. 

H.  &  B.  Hartinann  and  Braun,  Frankfort,  A.  M. 

J.  C.  Jules  Carpentier,  Paris,  France. 

J.  G.  B.  Jas.  G.  Biddle,  Philadelphia,  Pa. 

K.  &  W.  Jas.  White,  Glasgow,  Scotland. 

L.  M.  P.  L.  M.  Pignolet,  New  York,  N.  Y. 

L.  &N.  Leeds  and  Northrup  Co.,  Philadelphia,  Pa. 

M.  £  E.  Mayer  and  Englund,  Philadelphia,  Pa. 

M.  &  R.  Machado  and  Roller,  New  York,  N.  Y. 

M.  B.  F.  Co.  Meyers  Break  Finder  Co.,  Syracuse,  N.  Y. 

N.  E.  I.  Co.  Norton  Electrical  Inst.  Co.,  Manchester,  Conn. 

0.  W.  Otto  Wollff,  Berlin,  Germany. 

Q.  Co.  Queen  and  Co.,  Philadelphia,  Pa. 

R.  W.  P.  R.  W.  Paul,  London,  England. 

S.  &  H.  Siemens  and  Halske,  Berlin,  Germany. 

S.  E.  Co.  Sangaino  Electric  Co.,  Springfield,  111. 

S.  E.  I.  Co.  Syracuse  Electrical  Inst.  Co.,  Syracuse,  N.  Y. 

S.  E.  M.  Co.  Stanley  Electric  Mfg.  Co.,  Pittsfield,  Mass. 

W.  &  G.  Willy oung  and  Gibson  Co.,  New  York,  N.  Y. 

W.  E.  Co.  Western  Electric  Co.,  Chicago,  111. 

W.  E.  M.  Co.  Westinghouse  Elect.  &  Mfg.  Co.,  Pittsburg,  Pa. 

Wag.  E.  M.  Co.  Wagner  Elec.  Mfg.  Co.,  St.  Louis,  Mo. 

West.  E.  I.  Co.  Weston  Elec'l  Inst.  Co.,  Waverly  Park,  N.  J. 

Whit.  E.  I.  Co.  Whitney  Elec'l  Inst.  Co.,  Penacook,  N.  H. 


MAKERS   OR   AGENTS. 
FIG.  No. 

1  J.  C. 

3  L.  &  N.,  F.  P.  Co.,  W,  &  G.,  Q.  Co.,  S.  &  H.,  O. 

4  E.  B. 

5  W.  &  G.,  Q.  Co.,  L.  &  N.,  F.  P.  Co. 

6  ««  "          "  «« 

7  n  «  <« 

10  Q.  Co.,  J.  G.  B.,  K.  &  W. 

11  J.  C. 

14  Q.  Co.,  W.  &  G.,  L.  &  N.,  F.  P.  Co. 

15  West.  E.  I.  Co. 

16  Q.  Co.,  W.  &  G.,  L.  &  N.,  F.  P.  Co. 

20  Q.  Co.,  J.  G.  B.,  K.  &  W.,  H.  &  B. 

21  «  «»  «  « 

22  "  "  «« 

24  L.  &  N.,  Q.  Co.,  W.  &  G.,  J.  C. 

29  L.  &  N.,  Q.  Co.,  W.  &  G.,  F.  P.  Co. 

31  «  «i  «  « 

32  M.  &R.,  C.  &  A. 

36  Q.  Co.,  W.  &G.,  L.  &N. 


APPENDIX.  391 

FIG.  No. 


37 

L.  &N., 

Q.  Co.,  W.  &  G.,  W.  E.  Co.,  F.  P.  Co. 

40 

«« 

<<           «              «                      <« 

40A. 

C.  S.  I.  Co. 

44 

L.  &N., 

Q.  Co.,  W.  &  G.,  W.  E.  Co.,  F.  P.  Co. 

45 

« 

E.  V.  B., 

47 

« 

<«           i«              ««                      tt 

48 

H.  &B. 

49 

H.  &B. 

51 

L.  &  N., 

M.  &R.,  C.  &Co. 

52 

Q.  &  Co. 

,  L.  &N.,  W.  &G.,F.  P.  Co. 

53 

M.  &R., 

C.  &  Co. 

54 

J.  G.  B., 

C.  S.  I.  Co. 

55 

1  1, 

<  < 

56 

M.  &  R., 

C.  &  Co. 

57 

L.  &N. 

58 

0.  W.,  L 

.  &N.,  Q.    Co.,  W.  &G. 

59 

L.  &N. 

61 

Q,  Co.,  L.  &N.,  W.  &G. 

67 

<« 

"     F.  P.  Co.,  Whit.  E.  I.  Co. 

68 

*  < 

«                 « 

69 

Whit.  E. 

I.  Co. 

71 

O.  W. 

73 

E.  V.  B., 

L.  &N.f  Q.  Co.,  W.  &G. 

75 

L.  &N., 

Q.  Co.,  W.  &G. 

76 

Whit.  E. 

I.  Co. 

80 

E.  B. 

88 

M.  &R., 

C.  &  A. 

91 

L.  &N., 

Q.  Co.,  W.  &  G. 

92 

<  < 

««             « 

93 

<  < 

<t             « 

95 

" 

4'                               «« 

98 

Whit.  E. 

I.  Co. 

.99 

t  < 

100 

«« 

104 

Q.  Co. 

106 

Whit.  E. 

I.  Co. 

107 

L.  &N., 

Q.  Co.,  W.  &G. 

116 

J.  C.,  L. 

M.  P. 

118 

Whit.  E. 

I.  Co. 

119 

West.  E. 

I.  Co. 

120 

Whit.  E. 

I.  Co. 

121 

E.  E.  M. 

Co. 

122 

G.  E.  Co 

124 

«  « 

125 

<( 

126 

Q.  Co.,  L.  &  N.,  W.  &  G.,  F.  P.  Co. 

127 

H.  &B. 

129 

A.  E.  G.,  K.  &  W.,  W.  E.  M.  Co. 

392  APPENDIX 

FIG.  No. 

130  K.  &  W. 

131  " 

132  G.  E.  Co. 

133  Q.  Co.,  N.  E.  I.  Co.,  W.  E.  Co. 
137  H.  &  B.,  S.  E.  M.  Co. 

138 

139  Whit.  E.  I.  Co. 

140 

143  G.  E.  Co.,  W.  E.  M.  Co.,  Wag.  E.  M.  Co. 

145  Whit.  E.  I.  Co.,  A.  E.  G.,  H.  &  B. 

147  R.  W.  P.,  M.  &R. 

149  H.  &  B. 

150  A.  E.  G. 

151  G.  E.  Co. 
152 

153  W.  E.  M.  Co. 
154 

155  F.  W.  E.  Co. 

156  West.  E.  I.  Co. 

157  S.  E.  I.  Co.,  G.  E.  Co. 

158  C.  &  A.,  M.  &  R. 

159  G.  E.  Co..  W.  E.  M.  Co. 
160 

161  West.  E.  I.  Co.,  Whit.  E.  I.  Co. 

162  West.  E.  I.  Co. 

169  Whit.  E.  I.  Co. 

170  West.  E.  I.  Co. 

173  W.  E.  M.  Co.,  A.  E.  G. 

174 

179  West.  E.  I.  Co.,  Whit.  E.  I.  Co. 

185  L.  &  N.,  Q.  Co.,  W.  &  G.,  F.  P.  Co. 

187 

189 

194 

200 

206 

208 

209 

212  C.  S.  I.  Co.,  W.  &  G.,  J.  G.  B. 

213  W.  &G. 

214  H.  &B.,  M.  &R. 

215  «' 

216  W.  E.  M.  Co. 
ail7  A.  E.  G. 
218  H.  &  B. 

221  G.  E.  Co.,  W.  E.  M  Co 

222 

223  E.  D.  Co.,  West.  E.  I.  Co. 


APPENDIX.  393 


FIG.  No, 

238 

M.  B.  F.  Co. 

241 

B.  Co. 

242 

C.  &  A.,  M.  &R. 

243 

«       <  t 

244 

G.  E.  Co. 

245 

H.  &B.,  S.  &H. 

246 

C.  S.  I.  Co  ,  J.  G  B 

248 

C.  0. 

249 

« 

250-1 

West.  E.  I.  Co. 

257 

Whit.  E.  I.  Co. 

260 

G.  E.  Co.,  D.  M.  Co.,  D.  E.  M.  Co. 

262 

G.  E.  Co. 

265 

S.  E.  Co. 

271 

G.  I.  Co. 

274 

H.  &B. 

287 

J.  C. 

293 

S.  &H. 

294-5 

J.  C. 

302 

J.  C. 

304-5 

H.  &B. 

309 

E.  B. 

310 

J.  C. 

INDEX. 


Aaron  meter,  333. 

Absolute  capacity  measurement  with  gal- 
vanometer, 234. 

Accoustic  frequency  meter,  266. 

Air  condensers,  34,  234. 

Ammeters  for  both  direct  and  alternating 
current,  165. 

Ampere,  The,  2. 

Ampere  balance,  18. 

Arconi  recorder,  312. 

Armature  testing,  299. 

Atkinson  instruments,  168. 

Ayrton  shunt,  66. 

Ayrton  and  Perry  d.  c.  ammeter,  152. 

Ayrton  and  Perry  inductance  standard,  37. 

B.  A.  ohm,  2. 

B.  A.  form  of  standard  resistance,  11. 

Battery  resistance  by  half  deflection  method, 

146. 

Bell  magnet,  39. 
Bismuth  spiral,  350. 
Blondell  contactor,  261. 
Blondell  hysteresis  meter,  386. 
Bond  tester,  128. 
Boyle  integrator,  337. 
Boyle's  recorder,  315. 
Bristol  recorders,  304. 
Burger  permeameter,  379. 

Cadmium  cells,  27. 
Callendar  recorder,  310. 

Calibration  of  alternating  current  volt- 
meters, 213. 

of  ammeter,  methods  of,  189. 

of  slide  wires,  76. 

of  voltmeters,  209. 
Calibrating    voltmeters    with    Wheatstone 

bridge,  212. 

Calibration  of  wattmeter,  231. 
Capacity,  measurement  of,  234. 

by  direct  deflection,  239. 

by  loss  of  charge,  244. 

measurement  by  bridge  method,  240. 

measurement  by  divided  charge  method, 
239. 

measurement,    absolute,    with    galvano- 
meter, 234. 

Capillary  electrometers,  63. 
Carbon  megohms,  14. 

rheostats,  J87. 
Cardew  instruments,  174. 
Care  and  use  of  standard  cells,  28. 
Carhart  Clark  cell,  26. 
Carpentier  permeameter,  371. 
Chauvin  and  Arnoux  galvanometer,  50. 

recorders,  305. 


Clark  cell,  24. 

Classes  of  galvanometers,  38. 

of  recording  instruments,  304. 
Comparison  methods  of  measuring  capacity, 

236. 

Compass  test  for  fault  location,  294. 
Compensated  shunts,  65. 

voltmeters,  205. 

wattmeters,  227. 

Compensating   voltmeter  transformer,  207. 
Condenser  absorption,  246. 
Condensers,  34. 
Conductivity  bridges,  125. 
Connection  of  wattmeter,  225. 
Contact  devices,  78. 

troubles,  318. 
Copper  voltameter,  14,  16. 
Crompton  potentiometer,  80. 
Crosses  in  armatures,  301. 

on  lines,  297. 
Current,  measurement  of,  152. 

measurements  with  the  potentiometer,  88. 

regulating  devices,  186. 

Daniell  standard  cell,  29. 

D'arsonval  galvanometer,  46. 

Decade  pattern  Wheatstone  bridge,  99. 

Definition  of  units,  1. 

Deflectional    methods    of    measurement    of 
permeability,  369.  i 

Deprez-Carpentier  ammeter,  155. 

Determining  the  temperature  coefficient  of 
metals,  123. 

Divided  charge  method    of  capacity  meas- 
urement, 239. 

Divided  circuits,  law  of,  93. 

Dobrowolsky  phase  indicator,  270. 

Double  oscillograph,  264. 

Drysdale  permeameter,  361. 

Du  Bois  magnetic  balance,  368. 

Duddell  radiation  galvanometer,  60. 
oscillograph,  263. 

Dynamometer  voltmeters,  201. 
wattmeters,  218. 

Eddy  current  revolution  indicator,  278. 

Edison  chemical  meters,  325. 

Electrolytes,  measurement  of  resistance  of, 

by  alternating  current,  148. 
measurement  of  resistance  of,  by  secohm- 

meter    140. 
measurement  of  resistance  of,  by  Ayrton 

and  Perry  method,  143. 
Electromagnetic  instruments,  lt>7. 

voltmeters,  205. 
Electrostatic  ammeters,  179. 

voltmeters,  30,  197. 
395 


396 


INDEX. 


E.M.F.   measurement   by  drop   of  poten- 
tial, 23. 

by  potentiometer,  87. 
Erection  and  care  of  galvanometers,  68. 
Evershed  ohmmeter,  136. 
Ewing  balance,  367. 

hysteresis  meter,  383. 

permeameter,  374. 
Exploring  needle,  343. 

Fall  of  potential  method  for  ground  loca- 
tion, 296. 
Farad,  The,  4. 

Fessenden  contact  maker,  258. 
Field  strength,  determination  of,  by  oscil- 
lation of  a  magnet,  347. 
measurement   of,    by   ballistic   methods, 

358. 
measurement     of,     by     electromagnetic 

method,  351. 
measurement  of,   by  induction   method, 

349. 

by  calculation,  347. 
Fixed  coil  instruments,  152. 
Frequency  indicators,  265. 
meter,  accoustic,  266. 

Galvanometers,  38. 

Galvanometer  resistance  by  half  deflection 
method,  150. 

sensibility,  39. 

shunts,  64. 

suspensions,  41. 

Cans  and  Goldschmidt  instrument,  308. 
General  Electric  Co.  recorders,  306. 
German  silver,  10. 
Ground  detectors,  199. 
Grounds,  location  of,  by  induction  method, 

293. 
Guard  wires,  133. 

Hartmann   and   Brown   frequency  meters, 

265. 

hot  wire  instruments,  176. 
multicellular  voltmeters,  197. 
phase  indicator,  271. 
Henry,  The,  5. 

Bering's  liquid  potentiometer,  144. 
High  resistance  box,  13. 

resistances  measured  with  galvanometer 

and  voltmeter,  134. 
measurement  by  direct  deflection  method, 

131. 

by  leakage  method,  135. 
by  drop  of  potential  method,  136. 
sensibility  galvanometers,  49. 
Holden  instrument  for  hysteresis  measure- 
ment, 385. 

Hopkinson  divided  bar  method  of  measure- 
ment of  permeability,  359. 
Hotchkiss  oscillograph,  264. 
Hot  wire  ammeters,  174. 
galvanometers,  59. 
voltmeters,  205. 
wattmeters,  223. 


Hysteresis,  380. 

loss  by  wattmeter,  381. 
Hysteretic  losses,  measurement  of,  381. 

Impedance,  248. 
Inductance,  4. 

by  bridge  method,  248. 

by  calculation,  253. 

by  comparison  with  adjustable  standard, 
253. 

measurement  of,  247. 

method   of   measurement    with   secohm- 

meter,  252. 
Induction  ammeters,  181. 

wattmeters,  222,  336. 

method  of  locating  grounds,  293. 

method  of  measurement  of  field  strength 

349. 

Integrating  meters,  324. 
Intensity  of  magnetic  field,  344. 

of  magnetization,  346. 
Internal  resistance  of  batteries,  146. 

of  storage  batteries,  149. 
Inverted  Clark  cell,  26. 

Kelvin  ampere  balance,  165. 

ampere  gauges,  170. 

astatic  galvanometer,  57. 

balances,  22. 

galvanometer,  56. 

•    multicellular  electrostatic  voltmeter,  31. 
Kennelly  ammeter,  158. 
Kirchhoff  bridge,  115. 
Koepsel  permeameter,  370. 
Kohlrausch  bridge,  139. 

instruments,  167. 

Lambert  capacity  key,  244. 

Lamp  synchronizers,  273. 

Law  of  divided  circuits,  93. 

Leeds  and  Northrup  potentiometer,  81,  84. 

Legal  ohm,  2. 

Lincoln  synchronizer,  276. 

Location  of  breaks,  297. 

of  crosses  and  grounds,  288. 

of  faults,  288. 

of  open  circuits,  302. 
Lorenz  apparatus,  6. 
Low  resistance,  measurement  of,  114. 

measurement  with  an  ammeter,  117. 

measurement   by  Carey  Foster  method, 

122. 
Luminous  beam  for  reading  deflections,  44. 

Magnetic  induction,  345. 

moment,  345. 

vane  instruments,  172. 

units,  343. 

Magnetomotive  force,  345. 
Magnetometric  method  of  measurement  of 

permeability,  355. 
Magnetizing  force,  344. 
Mance's  method  of  measuring  battery  resis- 
tances, 146. 
Manganin,  10. 
Manzetti  frequency  meter,  268. 


INDEX. 


397 


Matthiessen  and  Hockin  bridge,  126. 

Maximum  demand  metera,  339. 

Maxwell's  method  of  measuring  inductance, 
249,  255. 

Mechanically  integrating  meters,  337. 

Metallic  alloy  standards,  9. 

Mercury  ohm,  6. 

Meyers  break  finder,  299. 

Mica  condensers,  35. 

Micro-ohmmeter,  120. 

Miot  inductiometer,  352. 

Modified  bridge  method  of  measuring  capac- 
ity, 242. 

Maxwell    method    for  inductance   measure- 
ments, 250. 

Moving  coil  galvanometers,  38,  46. 
instruments,  156. 
magnet  galvanometers,  38,  54. 

Miiller  synchronism  indicator,  274. 

Multiphase  ground  detectors,  199. 

Mutual  inductance,  254. 

by  Carey  Foster  method,  255. 

Murray  loop  test,  289. 

Nichols  method  of  measuring  inductance, 
254. 

Ohm,  The,  1. 

the  mercury  standard,  6. 

the  wire  standard,  1,1. 
Ohm's  law,  5. 
Ohmmeters,  107,  136. 
Ohmmeter  test  for  grounds,  290. 

Pellat  balance,  23. 

Permanent  magnet  voltmeters,  193. 

Permeability,  345. 

measurement  of,  354. 

measurement    by    attractional    methods, 
368. 

measurement  by  bridge  method,  371. 

by  magnetometric  method,  355. 

measurement    by    straight    bar,    ballistic 

test,  358. 

Permeameters,  374. 
Phase  indicators,  269. 
Picou  permeameter,  374. 
Platinum  silver,  10. 
Pole  strength,  343. 

Post-office  pattern  Wheatstone  bridge,  96. 
Potentials,  measurement  of,  193. 
Potential  indicators,  208. 
Potentiometers,  23,  73. 

Power  consumption  of  multiphase  circuits, 
229. 

measurement  of,  215. 
Properties  of  resistance  alloys,  10. 

Quantometer,  363. 
Quartz  filament,  39. 

Radial  arm  pattern  bridges,  101. 
Radiation  galvanometers,  60. 
Recording  instruments,  304. 
Reflecting  electro-dynamometers,  53. 

electrometers,  61,  195. 

galvanometer  scale  errors,  45. 


Relays,  320. 

Repulsion    electrostatic    ground    detectors, 

200. 
Resistance  alloys,  10. 

standards,  6. 

measurement  of,  93. 

measurement    with    voltmeter    and    am- 
meter, 112. 

measurement  with  a  potentiometer,  91. 

of  batteries,  146. 

of  electrolytes,  139. 

of  galvanometers,  149. 

coil  potentiometer,  82. 
Resistances  without  capacity  and  without 

inductance,  241. 
Reversed  coils,  location  of,  303. 
Rheostats,  water  cooled,  12,  188. 

wire,  186. 

Roller  hot  wire  instruments,  178. 
Rosa  curve  tracer,  259. 
Rowland  electro-dynamometer,  54. 
Rubbing  contacts,  319. 

Sangamo  integrating  meter,  330. 

Searle     method    of    measuring    hysteresis, 

386. 

Secohmmeter,  140,  252. 
Series  transformers,  183. 
Schattner  maximum  meter,  341. 
Schmidt  frequency  meter,  268. 
Scholkmann  speed  indicator,  280. 
Shallenberger  meter,  336. 
Shunted  ammeters,  162. 
Shunts,  162. 

galvanometer,  64. 
Siemens'  dynamometer,  165. 

ohm,  2. 

"Silver  voltameter,"  2. 
Slide-wire  bridges,  102. 

potentiometers,  73. 
Speed  indicators,  277. 
Speeds,  measurement  of,  by  stroboscopic 

methods,  280. 
Standards  of  capacity,  33. 
Standard  cells,  24. 
Standard  condensers,  34. 
Standards  of  inductance,  35. 
Standard  low  resistances,  89. 
Starting  coil  on  integrating  meters,  328. 
Station  potentiometer,  210. 
Stott  test  for  grounds,  294. 
Stroud  and  Henderson  method  of  measur- 
ing electrolytic  resistances,  141. 
Sumpner's    method    for   transformer   tests, 

282. 

Suppressed  scale  voltmeters,  207. 
Synchronism  indicators,  272. 
Synchronizing  by  lamps,  273. 

by  voltmeters,  274. 

Tangent  galvanometer,  16. 
Telephone  receiver,  62. 
Telescope,  42. 

Temperature  coefficients,  determination  of, 
123. 


398 


INDEX. 


Testing  for  grounds  in  an  armature,  300. 

integrating  meters,  285. 
Thermo-compensators,  164. 
Thompson  double  bridge,  119. 
Thompson's  method  of  measuring  galvano- 
meter resistance,  150. 
Thompson  method  of  mixtures,  243. 

permeameter,  364. 

"Varley  Slide,"  111. 
Thomson  ammeter,  159. 

inclined  coil  instruments,  171. 

integrating  meters,  327. 
Three-ammeter  method,  228. 

voltmeter  method,  227. 
Tractional  methods,  364. 
Transformer  insulation  tests,  283. 

polarity,  284. 

testing,  281. 


Unit  of  capacity,  4. 
of  current  strength,  2. 
of  electromotive  force,  3. 
of  inductance,  4. 
of  resistance,  1. 
magnetic  pole,  343. 


Varley  bridge,  109. 

loop  test,  291. 
Volt,  The,  3. 

balance,  32,  195. 

boxes,  87. 
Voltmeters,  193. 

Waddell  and  Legrand  recorder,  320. 
Water-cooled  rheostats,  12,  188. 
Watt  balance,  218. 
Wave  forms,  measurement  of,  257. 

form  determination  by  contact  methods, 
257. 

by  oscillograph  methods,  263. 
Weiss  galvanometer,  53. 
Weston  electrodynamometer  voltmeter,  201. 

d.  c.  ammeter,  156. 

recorder,  314. 

standard  cell,  27. 

wattmeter,  220. 
Wheatstone  bridge,  94. 

for  voltmeter  calibration,  212. 
Whitney  d.  c.  ammeter,  157. 

wattmeter,  218, 

Wire  rheostats,  186.  * 

Wright  maximum  meters,  339. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
This  book  is  DUE  on  the  last  date  stamped  below. 


OCT  19   1947 


25Jan'5C 


LD  21-100m-12,'46(A2012sl6)4120 


•11111 
I  ill  I 


I 

ran 


'.,/,:>• 


